Remember …
 What is the inverse of the following points? {(0, 2), (-1, 5), (-2, -6)}

√3
Solve sin-1 ( 2 ) = y
Aim: Convert between exponential & logarithmic equations.
Sometimes, things are not so simple: 10x = 9
We have a system in place to help us get pretty close to the true answer. To
undo exponents, we need to look at the inverse of exponents. We need
logarithms.
Logarithms can be referred to by their bases. The base of a logarithm is
indicated as a subscript after the word ‘log’.
Check out the reference table used before graphing calculators 
log
base
answer = exponent
Ex: Using the equation log 3 81 = 4, identify the following:
base:
exponent:
answer:
* If you don’t see a base, it is an invisible (common) 10.
1.
3.
log2 8 = 3
2.
log4 16 = 2
base:
base:
exponent:
exponent:
answer:
answer:
4.
1
log ( ) = -1
log12 144 = 2
10
base:
base:
exponent:
exponent:
answer:
answer:
Convert logarithm to exponential form:
logb y = x

bx = y
Write log2 8 = x in exponential form:
Rewrite the following in exponential form:
5.
log3 9 = 2
6.
log5 x = 3
7.
logb 81 = 2
8.
logx 36 = 2
We can now simplify expressions!
Simplify: log9 81
1. Set expression = x
2. Rewrite in exponential form
9.
Simplify log2 16
10.
Find the value of log2 8.
11.
Simplify log 10.
12.
Find the value of log3
Convert exponential form to logarithmic form:
bx = y
Rewrite 4-2 =
1
16

logb y = x
in logarithmic form.
Rewrite the following in logarithmic form:
13.
22 = 4
14.
5x = 7
15.
x4 = 5
16.
52 = y
The End
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