This document discusses the properties and laws of logarithms. It explains that common and natural logarithms have the same properties and laws, even though their bases differ. The key properties covered include: logarithms are only defined for positive values; ln1=0, ln e=1; and the product, quotient, and power laws. Several examples are worked through to demonstrate how to use these properties and laws to simplify logarithmic expressions and solve equations. The document emphasizes that understanding logarithmic properties and how to manipulate logarithms is important for advanced math, science, and engineering courses.
It includes concepts of logarithms including properties and log tables. The methodology to find out values using log tables and anti log tables is also mentioned in a detailed manner. Moreover, questions related to logarithms are mentioned for practice.
It includes concepts of logarithms including properties and log tables. The methodology to find out values using log tables and anti log tables is also mentioned in a detailed manner. Moreover, questions related to logarithms are mentioned for practice.
Had to make this dumb powerpoint for my algebra II class and I put a lot of work into it for some reason... so yeah it's just been sitting on my laptop doing nothing and I thought why not upload this to help other people? So yeah, hope you guys find it useful...
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!! :)
Shor's algorithm is for quantum computer. Using this algorithm any arbitrarily large number can be factored in polynomial time. which is not possible in classical computer
* Use the product rule for logarithms.
* Use the quotient rule for logarithms.
* Use the power rule for logarithms.
* Expand logarithmic expressions.
* Condense logarithmic expressions.
* Use the change-of-base formula for logarithms.
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16. Example
Using the quotient law,
write the given expression
as a single logarithm:
2
ln lnx x−
log(2 ) log( 1)x x− +
17. Try This
Using the quotient law, write
the given expression as a
single logarithm:
ln( 1) ln( 1)x x+ − −
1
ln
1
x
x
+
÷
−
18. Try This
Using the quotient law, write
the given expression as two
logarithms:
ln( 1) ln( 1)x x+ − −
1
ln
1
x
x
+
÷
−
19. Example
Using the power law, re-
write the given expression
and simplify if possible:
2
ln x 3log(2 )x
( 1)
ln( 1) x
x +
+ ( 1)ln( 1)x x+ +
20. Example
Using the power law, re-
write the given expression
and simplify if possible:
2
ln x 3log(2 )x
( 1)
ln( 1) x
x +
+ ( 1)ln( 1)x x+ +
21. Try This
Using the power law, re-
write the given expression
and simplify if possible:
2
log4
3
lne
5
log10
2log4
3ln 3e =
5log10 5=
22. Example
Use a combination of
logarithmic properties and
laws to re-write the given
expression:
2
2( 3)
ln
1
x
x
+
÷
−
23. Example
Use a combination of
logarithmic properties and
laws to re-write the given
expression:
3
10
log
1
x
x
÷
+
24. Try This
Use a
combination of
logarithmic
properties and
laws to re-
write the given
expression:
3
( 5)
ln
1
e x
x
−
÷
+
1 3ln( 5) ln( 1)x x+ − − +
25. Example
The 1989 world series
earthquake in San Francisco
measure 7.0 on the Richter
Scale. The great earthquake
of 1906 measured 8.3. How
much more intense was the
1906 quake?
( )0logR i i=
26. Example
Decibels are calculated by
the function where
is the minimum sound
intensity detectable by the
human ear. Find the decibel
level of a jet engine which is
10 billion times
010log( )i i
0i
0.i
27. Lesson Close
The manipulation of
logarithms is a fundamental
math skill that you will need
in upper level math courses
and in science and
engineering.