1. Aim: What is the common logarithms?
Do Now: Evaluate the following
log10 1
log1010
log10 100
log 5.
HW: p.335 # 8,20,22,28,32,38,42,50,54,56

2. In log a, the value of a must be greater than 0
Any logarithm with base 10 is called common log
We can write log10 a as log a, that is if the base of a logarithm is not indicated, then its base is 10
Use calculator to find the value of common log
1. log 2.53
2. log 0.8
3. log 0
4. log -2
3. undefined
4. undefined
In log a, the value of a must be greater than 0

3. If log x = 3.7886, find x to the nearest integer
If log a = , find log 0.001a
Use product rule: log 0.001a = log log a
= –
= –2.4267

4. If log N = 3.36486, find N to the nearest integer
= 2317
Evaluate log2 6
Since the calculator does not have give log base 2 ,we need to rewrite log2 6 with base 10
Use the formula

5. Express log N in terms of log x, log y and log z

6. If log 7.11 = b, then log 7110 equals
a) 1000b b) 3b c) 3 + b d) b
log 7110 = log (7.11 • 1000)
= log log 1000
= b + 3
The expression is equivalent to

7. c 1. Find N to the nearest tenth: log N = .6884 N = 4.9
3. If log x = , find x to the nearest tenth
x = 76.5
4. If log a = c, then log 100a equals
a) 110c b) 2c c) 2 + c d) 2 + log c c
5. The expression is equivalent to b