The document discusses properties of logarithms. It begins by recalling rules of exponents and their corresponding rules of logarithms. Four basic logarithm rules are presented: 1) logb(1) = 0, 2) logb(xy) = logb(x) + logb(y), 3) logb(x/y) = logb(x) - logb(y), 4) logb(xt) = tlogb(x). It then works through an example problem to demonstrate using these rules to write the logarithm of a expression in terms of logarithms of its variables. It concludes by noting that logarithms and exponentials are inverse functions, so logb(bx) =
Lots of students find logarithm complicated and tricky.For them this slide may prove useful.This is the most easy way to learn logarithm.Best of luck!! :)
Daffodil International University is a co-educational private university located in Dhanmondi, Dhaka, Bangladesh. It was established on 24 January 2002 under the Private University Act, 1992
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
#6 - LOGARITHMS
LOG of a POWER
LOG of a ROOT
PROOFS
ANTILOGARITHMS
INVERSE OPERATIONS
NATURAL LOGARITHMS
NEPER - NAPIER - EULER'S NUMBER
LOG - LN
POWER - ROOT
PRODUCT - QUOTIENT
CHANGE of BASE
PROOFS - EXAMPLES
CALCULATIONS STEP by STEP
MATHS SYMBOLS
www.enzoexposito.it/mobile/matematica.html
www.enzoexposito.it/mobile/expon_log.html
logarithmic, exponential, trigonometric functions and their graphs.pptYohannesAndualem1
Introduction:
[Start with a brief introduction about yourself, including your profession or main area of expertise.]
Background:
[Discuss your background, education, and any relevant experiences that have shaped your journey.]
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[Highlight notable achievements, awards, or significant projects you've been involved in.]
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[Detail your areas of expertise, skills, or specific knowledge that sets you apart in your field.]
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[Share your passions, hobbies, or interests outside of your professional life, adding depth to your personality.]
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[If applicable, articulate your vision, mission, or goals in your chosen field or in life in general.]
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[End with a closing statement that summarizes your essence or leaves a lasting impression.]
Feel free to customize each section with your own personal details and experiences. If you need further assistance or have specific points you'd like to include, feel free to let me know!
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Let's dive deeper into the world of ODC! Ricardo Alves (OutSystems) will join us to tell all about the new Data Fabric. After that, Sezen de Bruijn (OutSystems) will get into the details on how to best design a sturdy architecture within ODC.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
3. 1. b0
= 1
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
4. 1. b0
= 1
2. br
· bt
= br+t
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
5. 1. b0
= 1
2. br
· bt
= br+t
3. = br-t
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
6. 1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
7. 1. logb(1) = 01. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
8. 1. logb(1) = 0
2. logb(x·y) = logb(x)+logb(y)
1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
9. 1. logb(1) = 0
2. logb(x·y) = logb(x)+logb(y)
3. logb( ) = logb(x) – logb(y)
x
y
1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
10. 1. logb(1) = 0
2. logb(x·y) = logb(x)+logb(y)
3. logb( ) = logb(x) – logb(y)
4. logb(xt
) = t·logb(x)
x
y
1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
11. 1. logb(1) = 0
2. logb(x·y) = logb(x)+logb(y)
3. logb( ) = logb(x) – logb(y)
4. logb(xt
) = t·logb(x)
x
y
1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
We veryify part 2: logb(xy) = logb(x) + logb(y), x, y > 0.
Proof:
12. 1. logb(1) = 0
2. logb(x·y) = logb(x)+logb(y)
3. logb( ) = logb(x) – logb(y)
4. logb(xt
) = t·logb(x)
x
y
1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
We veryify part 2: logb(xy) = logb(x) + logb(y), x, y > 0.
Proof:
Let x and y be two positive numbers.
13. 1. logb(1) = 0
2. logb(x·y) = logb(x)+logb(y)
3. logb( ) = logb(x) – logb(y)
4. logb(xt
) = t·logb(x)
x
y
1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
We veryify part 2: logb(xy) = logb(x) + logb(y), x, y > 0.
Proof:
Let x and y be two positive numbers. Let logb(x) = r
and logb(y) = t, which in exp-form are x = br
and y = bt
.
14. 1. logb(1) = 0
2. logb(x·y) = logb(x)+logb(y)
3. logb( ) = logb(x) – logb(y)
4. logb(xt
) = t·logb(x)
x
y
1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
We veryify part 2: logb(xy) = logb(x) + logb(y), x, y > 0.
Proof:
Let x and y be two positive numbers. Let logb(x) = r
and logb(y) = t, which in exp-form are x = br
and y = bt
.
Therefore x·y = br+t
,
15. 1. logb(1) = 0
2. logb(x·y) = logb(x)+logb(y)
3. logb( ) = logb(x) – logb(y)
4. logb(xt
) = t·logb(x)
x
y
1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
We veryify part 2: logb(xy) = logb(x) + logb(y), x, y > 0.
Proof:
Let x and y be two positive numbers. Let logb(x) = r
and logb(y) = t, which in exp-form are x = br
and y = bt
.
Therefore x·y = br+t
, which in log-form is
logb(x·y) = r + t = logb(x)+logb(y).
16. 1. logb(1) = 0
2. logb(x·y) = logb(x)+logb(y)
3. logb( ) = logb(x) – logb(y)
4. logb(xt
) = t·logb(x)
x
y
1. b0
= 1
2. br
· bt
= br+t
3. = br-t
4. (br
)t
= brt
bt
br
Properties of Logarithm
Recall the following
Rules of Exponents:
The corresponding
Rules of Logs are:
We veryify part 2: logb(xy) = logb(x) + logb(y), x, y > 0.
Proof:
Let x and y be two positive numbers. Let logb(x) = r
and logb(y) = t, which in exp-form are x = br
and y = bt
.
Therefore x·y = br+t
, which in log-form is
logb(x·y) = r + t = logb(x)+logb(y).The other rules may be verified similarly.
18. 3x2
√y
log( ) = log( ),3x2
√y
3x2
y1/2
Properties of Logarithm
a. Write log( ) in terms of log(x) and log(y).
Example A:
19. 3x2
√y
log( ) = log( ), by the quotient rule
= log (3x2
) – log(y1/2
)
3x2
√y
3x2
y1/2
Properties of Logarithm
a. Write log( ) in terms of log(x) and log(y).
Example A:
20. 3x2
√y
log( ) = log( ), by the quotient rule
= log (3x2
) – log(y1/2
)
product rule
= log(3) + log(x2
)
3x2
√y
3x2
y1/2
Properties of Logarithm
a. Write log( ) in terms of log(x) and log(y).
Example A:
21. 3x2
√y
log( ) = log( ), by the quotient rule
= log (3x2
) – log(y1/2
)
product rule power rule
= log(3) + log(x2
) – ½ log(y)
3x2
√y
3x2
y1/2
Properties of Logarithm
a. Write log( ) in terms of log(x) and log(y).
Example A:
22. 3x2
√y
log( ) = log( ), by the quotient rule
= log (3x2
) – log(y1/2
)
product rule power rule
= log(3) + log(x2
) – ½ log(y)
= log(3) + 2log(x) – ½ log(y)
3x2
√y
3x2
y1/2
Properties of Logarithm
a. Write log( ) in terms of log(x) and log(y).
Example A:
23. 3x2
√y
log( ) = log( ), by the quotient rule
= log (3x2
) – log(y1/2
)
product rule power rule
= log(3) + log(x2
) – ½ log(y)
= log(3) + 2log(x) – ½ log(y)
3x2
√y
3x2
y1/2
Properties of Logarithm
a. Write log( ) in terms of log(x) and log(y).
b. Combine log(3) + 2log(x) – ½ log(y) into one log.
Example A:
24. 3x2
√y
log( ) = log( ), by the quotient rule
= log (3x2
) – log(y1/2
)
product rule power rule
= log(3) + log(x2
) – ½ log(y)
= log(3) + 2log(x) – ½ log(y)
3x2
√y
3x2
y1/2
Properties of Logarithm
a. Write log( ) in terms of log(x) and log(y).
log(3) + 2log(x) – ½ log(y) power rule
= log(3) + log(x2
) – log(y1/2
)
b. Combine log(3) + 2log(x) – ½ log(y) into one log.
Example A:
25. 3x2
√y
log( ) = log( ), by the quotient rule
= log (3x2
) – log(y1/2
)
product rule power rule
= log(3) + log(x2
) – ½ log(y)
= log(3) + 2log(x) – ½ log(y)
3x2
√y
3x2
y1/2
Properties of Logarithm
a. Write log( ) in terms of log(x) and log(y).
log(3) + 2log(x) – ½ log(y) power rule
= log(3) + log(x2
) – log(y1/2
) product rule
= log (3x2
) – log(y1/2
)
b. Combine log(3) + 2log(x) – ½ log(y) into one log.
Example A:
26. 3x2
√y
log( ) = log( ), by the quotient rule
= log (3x2
) – log(y1/2
)
product rule power rule
= log(3) + log(x2
) – ½ log(y)
= log(3) + 2log(x) – ½ log(y)
3x2
√y
3x2
y1/2
Properties of Logarithm
a. Write log( ) in terms of log(x) and log(y).
log(3) + 2log(x) – ½ log(y) power rule
= log(3) + log(x2
) – log(y1/2
) product rule
= log (3x2
) – log(y1/2
)= log( )3x2
y1/2
b. Combine log(3) + 2log(x) – ½ log(y) into one log.
Example A:
27. Recall that given a pair of inverse functions, f and f -1
,
then f(f -1
(x)) = x and f -1
(f(x)) = x.
Properties of Logarithm
28. Recall that given a pair of inverse functions, f and f -1
,
then f(f -1
(x)) = x and f -1
(f(x)) = x.
Since expb(x) and logb(x) is a pair of inverse functions,
Properties of Logarithm
29. Recall that given a pair of inverse functions, f and f -1
,
then f(f -1
(x)) = x and f -1
(f(x)) = x.
Since expb(x) and logb(x) is a pair of inverse functions,
we have that:
a. logb(expb(x)) = x or logb(bx
) = x
Properties of Logarithm
30. Recall that given a pair of inverse functions, f and f -1
,
then f(f -1
(x)) = x and f -1
(f(x)) = x.
Since expb(x) and logb(x) is a pair of inverse functions,
we have that:
a. logb(expb(x)) = x or logb(bx
) = x
b. expb(logb(x)) = x or blog (x)
= x
Properties of Logarithm
b
31. Recall that given a pair of inverse functions, f and f -1
,
then f(f -1
(x)) = x and f -1
(f(x)) = x.
Since expb(x) and logb(x) is a pair of inverse functions,
we have that:
a. logb(expb(x)) = x or logb(bx
) = x
b. expb(logb(x)) = x or blog (x)
= x
Properties of Logarithm
b
Example B: Simplify
a. log2(2-5
) =
b. 8log (xy)
=
c. e2+ln(7)
=
8
32. Recall that given a pair of inverse functions, f and f -1
,
then f(f -1
(x)) = x and f -1
(f(x)) = x.
Since expb(x) and logb(x) is a pair of inverse functions,
we have that:
a. logb(expb(x)) = x or logb(bx
) = x
b. expb(logb(x)) = x or blog (x)
= x
Properties of Logarithm
b
Example B: Simplify
a. log2(2-5
) = -5
b. 8log (xy)
=
c. e2+ln(7)
=
8
33. Recall that given a pair of inverse functions, f and f -1
,
then f(f -1
(x)) = x and f -1
(f(x)) = x.
Since expb(x) and logb(x) is a pair of inverse functions,
we have that:
a. logb(expb(x)) = x or logb(bx
) = x
b. expb(logb(x)) = x or blog (x)
= x
Properties of Logarithm
b
Example B: Simplify
a. log2(2-5
) = -5
b. 8log (xy)
= xy
c. e2+ln(7)
=
8
34. Recall that given a pair of inverse functions, f and f -1
,
then f(f -1
(x)) = x and f -1
(f(x)) = x.
Since expb(x) and logb(x) is a pair of inverse functions,
we have that:
a. logb(expb(x)) = x or logb(bx
) = x
b. expb(logb(x)) = x or blog (x)
= x
Properties of Logarithm
b
Example B: Simplify
a. log2(2-5
) = -5
b. 8log (xy)
= xy
c. e2+ln(7)
= e2
·eln(7)
= 7e2
8
