5.4 Equations Involving Logarithms

METHOD:

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

Example 1
Solve the following equation:
(a) ${\log }_{3}2+{\log }_3(x+5)={\log }_3(3x-1)$
(b) ${\log }_{2}8x-3={\log }_2(2x-1)$
(c) $3{\log }_{x}2+2{\log }_{x}4-{\log }_{x}256=-1$