Rewriting exponential form to logarithm form and back. Solve logarithm equations.

1. Day 3
Common
Logarithms

2. Express each number using exponents.
O A. 36 G. 1
O B. 121 What about . . .
O C. 4 H. 345
O D. I. 0.0023
O E. 100
O F. 1000

3. Logarithms give you a way to
solve for an exponent.
O Ex: 5x = 12
Common Logarithms are any
logarithm of base 10
Ex: log10 or log

4. Rewriting:
10b = a log10a=b
A. 102 = 100
B. 33 = 27
C. 25 = 32
log10 100 = 2
log3 27 = 3
log2 32 = 5

5. E. 641/2 = 8
F. log6 36 = 2
Log64 8 = 1/2
D. 9-2 =
1
81
G. log3 81 = 4
H. log14 = -2
1
196
I. log10 10 = 1
J. Log 1 = 0
Log9 = -2
1
81
62 = 36
34 = 81
101 = 10
100 = 1
14-2 =
1
196

6. Evaluate without a calculator:
A. Log4 64
Step 1: set = to x Log4 64 = x
Step 2: rewrite in
exp. form
4x = 64
Step 3: break down
the #’s
22x = 26
Step 4: once the bases
are the same,
set exp. =
2x = 6
x = 3

7. B) Log5 125
5x = 125
5x = 55
x = 5
C) Log4 16
4x = 16
22x = 24
2x = 4
x = 2

8. D) Log343 7
343 = 7x
73x = 71
x = 1/3
Log343 7 = x
3x = 1

9. E) Log3
3x = 3-5
Log3 = x
x = -5
243
1
3x = 243
1
243
1

10. Evaluate using a calculator.
A) Log 75 1.8751
B) Log -3 Not possible
** log10 (-3) = x
10x = -3
C) Log 1 0
** log10 1= x 10x = 1

11. But what if the base isn’t 10?
Use Change of Base Formula:
logb a = or

12. A) log5 3 log 3
log 5
= 0.6826
B) log11 18 log 18
log 11
= 1.2054
C) log4 8
log 8
log 4 = 1.5