6.5 Applications of Common Logarithms
Objectives: Define and use the common logarithmic
function to solve exponential and logarithmic equations.
Evaluate logarithmic expressions by using the
change-of-base formula.
Standard: 2.8.11.N. Solve exponential equations.
Warm Up:
1.51
103  v
v  .001
0.25
-2.30
v  49
16v  4
v 7
(42 )v  4
2
2
v7
2
42 v  41
2v  1
1
v
2
The base 10 logarithm is called the
common logarithm.
In general, logarithmic functions are used
to assign large values in the domain to
small values in the range.
x
10
100
y = log x
1
2
1000
3
10,000 100,000
4
5
…
…
Recall from lesson 2.7 that the graph of y = a*f(x)
is the graph of y = f(x) stretched by a factor of a.
Therefore the graph of y = 10 log x is the graph
of y = log x stretched by a factor of 10.
R  10log
300 I 0
I0
R  10log 300
R  25 decibels
R  10log
I
I0
107 
70  10 log
I
I0
10 log
I
I0
70

10
10
7  log
I
I0
I
I0
107 I0  I
The running vacuum cleaner is about
107 , or 10,000,000
times as loud as the threshold of hearing.
log8  log 792
x
x
log8  log 792
log 792
x=
log 8
x  3.21
You can use the change-of-base
formula to change a logarithmic
expression of any base to base 10
so that you can use the LOG key
on your calculator.
log 36
log8 36 
log 8
p. 389 #10-16 even
p. 390: #28-34 Even
Homework:
Practice 6.5
Chapter 6 Test FRIDAY!