SOLVING LOGARITHMIC EQUATIONS
A logarithmic equation can be solved by expressing it in exponential form
and solving the resulting exponential equation.
Recall…
y = logax is only defined for x > 0
Therefore, when solving log equations,
answers where x  0 are inadmissible.
Example 
Solve each of the following:
a)
1 
log x    2
 25 
b)
log6(2x – 1) = log69
c)
log23 + log2x = log218
d)
log324x – log38 = 4
e)
log427 = 3log4x
f)
log2(x + 2) + log2(x – 1) = 2
A solution is inadmissible
if its substitution in the
original equation results in
an undefined value!!
Summary
When solving a logarithmic equation:



Example 
simplify using the laws of logarithms
if logaM = logaN, then M = N, where a, M, N > 0
check for inadmissible solutions
A Richter scale is used to compare the intensities of earthquakes.
The Richter scale magnitude, R, of an earthquake is determined
using the given equation, where a is the amplitude of the vertical
ground motion in microns (), T is the period of the seismic wave in
seconds, and B is a factor that accounts for the weakening of the
seismic waves. An earthquake measured 5.5 on the Richter scale,
and the period of the seismic wave was 1.8s. If B equals 3.2,
determine the amplitude of the vertical ground motion.
a
R  log    B
T
Note: 1  = 10–6 m
Homework: p.491–492
#1–7, 10, 17, 19