$log_a$(b) = log_c$$\frac{b}{log_c}(a) for any valid base c. Special cases: $log_a$(b) = 1/$log_b$(a), and the chain rule $log_a$(b)$log_b$(c) = $log_a$(c). These allow converting between any bases. For computation, convert everything to $log_{10}$ or ln. The chain rule is particularly useful: $log_2$(3)$log_3$(5)*$log_5$(8) = $log_2$(8) = 3.