Converting to logarithm What logarithm rule can convert:

$$\left(\frac n4\right)^i = 1$$

to:

$$i = log_4(n)$$

When I view cheat-sheets for logarithm rules, I only see conversions where both sides of the equation have log in it. Thank you.
The basic rule

$$\log_ax^n=n\log_ax$$

so

$$\left(\frac n4\right)^i=1\iff i\log\frac n4=\log 1=0$$

What you have seems to be incorrect, thus.
No rule can get you from the first equation to the second. What is true is that
$$\begin{align}
0=\log_41&amp;=\log_4\left(\left(\frac{n}{4}\right)^i\right)\\
  &amp;=i\log_4\left(\frac{n}{4}\right)\\
  &amp;=i(\log_4n-\log_44)\\
  &amp;=i(\log_4n-1)
\end{align}$$
and this is only satisfied when $i=0$ or $n=4$ (which makes perfect sense by looking at your first equation).