Exponential equations are solved by substitution: set t = $a^x$ (note t > 0). Example: 9^x - 43^x + 3 = 0 becomes $t^2$ - 4t + 3 = 0 (where t = 3^x), giving t = 1 or t = 3, so x = 0 or x = 1. For equations involving both $a^x$ and a^(-x): set t = $a^x$ so a^(-x) = 1/t, multiply through by t to clear fractions. Discard negative t values since $a^x$ > 0 always. For equations like 2^x = 3^x: divide both sides by 3^x to get $\frac{2}{3}$^x = 1, so x = 0. If 2^x = 32^(-x): set t = 2^x, get $t^2$ = 3, t = sqrt(3), x = $log_2$(sqrt(3)) = $\frac{1}{2}$*$log_2$(3).