Exponential and Logarithmic Equations and Inequalities

2.13A solved equations with the unknown in an exponent. Now the unknown sits inside a logarithm, as in $\log_{2} x + \log_{2}(x - 2) = 3$. The algebra uses the same tools, rewriting between log and exponential form (2.9) and the log rules (2.12), but there is one new danger. The log rules can turn an equation into one with EXTRA solutions that don't work in the original. Checking every answer is not optional here.