The document discusses the applications of logarithmic and exponential functions in real-life scenarios such as measuring earthquake magnitudes, sound intensity, acidity, population growth, and compound interest. It highlights how logarithmic functions simplify complex data, while exponential functions model rapid growth or decay phenomena. Mathematics is emphasized as a critical tool in everyday life across various fields.

1. LOGARITHM AND
EXPONENETIAL
FUNCTIONS
PRESENTATION MADE
AREEBA JUNAID

2. Contents::
. APPLICATION OF MATHS IN REAL LIFE
. LOGARITHM FUNCTIONS
1) MAGNITUDE OF EARTH
2) INTENSITY OF SOUND
3) ACIDITY OF LIQUID
4)COMPUTER PROGRAMS
. EXPONENTIAL FUNCTION
1) TO STUDY GROWTH
2) HALF LIFE
3)COMPOUND INTEREST

3. APPLICATION OF MATHS IN REAL LIFE
 Mathematics is the cradle of all creation , without which
the world cannot move an inch. Be it a cook or a farmer
,a carpenter or a mechanics, an engineer or a scientist ,a
musician or a magician, everyone needs mathematics in
their day-to-day life.
 Moths underline every process and pattern that occurs
in this world
 It is a tool in our hands to make our life simpler and
easier .

4. INTRODUCTION:
LOGARITHM FUNCTION:
Logarithmic can be used to model real-world situations.
Logarithmic functions are very helpful when working with
phenomena that have a very wide range of values because
logarithm functions have the ability to capture large variety of
inputs in a relatively small range of outputs.
EXPONENTIAL FUNCTION:
Exponential functions are helpful with phenomena that change
very quickly, or that grow or decay by a percentage over a
particular time period. In short, Exponential function allow us to
describe the growth (or decay) of a quantity whose rate of
change is related to its current value.

5. APPLICATIONS:
 MAGNITUDE OF EARTHQUAKE:
Logarithmic function is used to measure
the magnitude & intensity of earthquakes. The
magnitude of an earthquake is a Logarithmic scale. The
magnitude of an earthquake is related to how much
energy is released by the quake.
The famous "Richter Scale" uses this formula:
M = log10 A + B
seismographs detect
movement in the earth

6.  MEASURING ACIDITY OF LIQUID:
 The Real life scenario of logarithms is used to find
,basic and neutral of the substance) which is based on the
amount of hydrogen ions (H+) in the liquid.
 pH is an incredibly important parameter that is measured
nearly every water quality application. It plays a role in the
taste (acid = fresh, neutral = bland, and alkaline =
and the preservation of food. In environmental sampling
and monitoring, high or low pH values can be indicative of
pollution. In wastewater treatment, pH is regulated as part
an NPDES permit and many processes are pH dependent
 The formula for pH is:
pH = −log[H+]

7. DETERMINING LOUDNESS & INTENSITY OF
SOUND:
 We are able to hear sounds ranging from what you
call extremely quiet to extremely loud; the change in
actual power level is vast. So we use logarithms to
the range of possible sound or sound intensity much
compactly
 A logarithmic scale is standard for
measuring the perceived loudness of sound. The
perceived loudness of sound is basically proportional to
the logarithm of the actual power being transmitted
through the air.
 Sound is measured in a logarithmic scale using a
unit called a decibel
 Loudness in dB = 10 log10 (p × 1012)

8. COMPUTER PROGRAMS:
 Logarithms simplify complicated numbers through exponents and
coefficients. Log tables help you to refer the corresponding numbers and
make calculations less laborious because of these reasons It is largely
used in computing memory spaces and in computer languages
 Computer developers use logarithms in computer function formulas to
create specific software program outcomes, such as the creation of graphs
that compare statistical data

9. TO STUDY GROWTH:
 Exponential function is used to model situations in which
growth begins slowly and then accelerates rapidly without
bound, following are the examples of things which grow
rapidly
1) POPULATION GROWTH:
Exponential functions are quite commonly used to
model population growth .The population of earth can
be modelled by a simple exponential function. Which is useful
for determining number of deaths and births per year
Below is an interactive demonstration of the
population growth of a species of rabbits whose population
grows at 200% each year and demonstrates the power of
exponential population growth.

10. 2) PANDEMIC SITUATION:
 IN Devastating situation of pandemic exponential function
is useful for determining the rate with which pandemic can
spread In short, exponential growth can potentially be used
to combat and mitigate bad information.
 growth of phenomena such as virus infections, Internet
usage, and popularity of fads can also be determine using
exponential function

11. COMPOUND INTEREST:
 Compound interest (or compounding interest) is
interest calculated on the initial principal, which
includes all of the accumulated interest from
previous periods on a deposit or loan. compound
interest can be thought of as "interest on interest,"
and will make a sum grow at a faster rate
than simple interest.
 One real world application of exponential
is in compound interest because Compound
interest gives exponential growth because
the growth increases at an increasing, or
accelerated rate The formula for compound
with a finite number of calculations is an
exponential equation

12. FUN FACT:
"Google gives every page on the web a
score (PageRank) which is a rough measure
of authority / importance. PageRank is an
algorithm used by Google Search to rank
web pages in their search engine results.
This is a logarithmic scale"