Question

4^9n+4=256

Answer 1

\(\bf \large 4^{9n}+4=256 \quad ?\)

Answer 2

Nope. 4+^9n+4 (<-- All to the power of)
The only numbers that aren't powers are the first "4" and the "256" at the end.

Does that help?

Answer 3

\(\bf \large {4^{9n+4}=256\\ \quad \\
\textit{let us use the log cancellation rule of }\quad log_aa^x = x\\ \quad \\
4^{9n+4}=256\implies log_4(4^{9n+4})=log_4(256)\\\quad \\\implies 9n+4=log_4(256)\\ \quad \\
9n = log_4(256)-4\implies n = \cfrac{log_4(256)-4}{9}}\)