Solving a 'Stanford' University entrance exam | t=?

To solve exponential equations like 9^t × 27^t = 300, express all bases as powers of the same base (9 = 3², 27 = 3³), combine exponents using (a^m)^n = a^(mn) and a^m × a^n = a^(m+n) to get 3^(5t) = 300, then take logarithms on both sides and apply log properties (log(m^n) = n·log(m), log(mn) = log(m) + log(n), log(m)/log(n) = log_n(m)) to solve for t, yielding t = (1 + 2log₃(5) + 2log₃(2))/5.