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 (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)) = (1/2)*log_2(3).