Chapter 8

EXAMPLE 4
Selecting a strategy to evaluate common
logarithms
Use the log key on a calculator to evaluate the following logarithms. Explain
how the calculator determined the values.
a) log 10 b) log 100 c) log 500
Solution
Notice that no base is given with the
logarithms. Recall that log x 5 log 10 x.
a) log 10 10 5 x
10 x 5 10, so x 5 1
b) log 10 100 5 x
10 x 5 100, so x 5 2
c) log 10 500 5 x
10 x 5 500, so x 8 2.7
Let x represent the value of each
expression. Rewrite each equation in
exponential form.
The calculator determined the exponents that must be applied to base 10 to get
10, 100, and 500.
EXAMPLE 5
Examining some general properties
of logarithms
Evaluate each of the following logarithms.
a) log 6 1 b) log 5 5 x c)
Solution
6 log 6x
a)
log 6 1 5 0
log 6 1 5 x
6 x 5 1
6 x 5 6 0
x 5 0
The value of the expression is the
exponent to which 6 must be raised
to get 1. A power equals 1 only when
its exponent is 0.
To verify, let the expression equal x
and rewrite the expression in
exponential form.
464 8.3 Evaluating Logarithms
NEL