# 5.4 Equations Involving Logarithms

METHOD:
1. For two logarithms of the same base, if ${\mathrm{log}}_{a}m={\mathrm{log}}_{a}n$ , then m = n
2. Convert to index form, if ${\mathrm{log}}_{a}m=n$ , then m = an.

Example 1
Solve the following equation:
(a) ${\mathrm{log}}_{3}2+{\mathrm{log}}_{3}\left(x+5\right)={\mathrm{log}}_{3}\left(3x-1\right)$
(b) ${\mathrm{log}}_{2}8x-3={\mathrm{log}}_{2}\left(2x-1\right)$
(c) $3{\mathrm{log}}_{x}2+2{\mathrm{log}}_{x}4-{\mathrm{log}}_{x}256=-1$