1. Objectives:
1. Rewrite log equations
2. Evaluate logarithms
3. Solve log equations

2. know 22 = 4 and 23 = 8, but for
what value of x does 2x = 6?
It must be between 2 and 3…
Logarithms were invented to
solve exponential equations like
this.
x = log26 ≈ 2.585
We

3. Let
b and y be positive numbers
and b≠1.
The logarithm of y with base b is
written logby and is defined:
logby = x if and only if bx = y

4. Common
Logarithm - the log with
base 10
 log10 x = log x
Natural
Logarithm – the log with
base e
 loge x = ln x

5. Use the “circle cycle” to “chop off the
log!”
Write these in exponential form:
log2
32 = 5
log5 1
=0
log 10
=1
 ln
0.2 ≈ -1.6

6. To
find logb y, think
“b to what power will give me y?”
Examples:
log3
81
log1/2
log9
8
3

7. Find
log4
each logarithm:
64
log32
log
2
100

8. Find
the value of x to the nearest
hundredth:
10x = 170
ex
= 500

9. Solve
for x to the nearest
hundredth.
10x = 50
ex
= 50

10. To solve: rewrite in exponential
form, then simplify.
Solve without a calculator:
log5 x = 2
log
ln
x=2
|x| = 2

11. Solve:
log6
ln
x=2
x=2