Base Switch

The logarithmic base switch rule simply states that given a base and an argument to a log function. The inverse of that base is simply the reciprocal of the log.

\[ log_a(b) = \frac{1}{logb(a)} \]

For example, if we know \( log_2(16) = 4 \) but we want to know \( log_16(2) \), essentially the inverse of raising \(2^4 \) we can simply take the recriprocal of \( 4 \). So,

\[ log_16(2) = \frac{1}{log_2(16)} \]