Natural logarithm over natural logarithm

Question

How are you supposed to simplify a natural log over another natural log?

Ex.

$$\frac{\ln(64)}{\ln(4)}.$$

Answer 1

One logarithm divided by the other is equivalent to a change of base of the logarithm:

$$\ln(a)\div\ln(b) = \log_b(a)$$

Do you know what $\log_4(64)$ is?

Answer 2

\begin{align} \frac{\ln (64)}{\ln (4)}=\frac{\ln (4^3)}{\ln (4)} \end{align}

Note that $\log a^b= b \log a$