Question

6^3 = 2^n + 3^n solve for n

Answer 1

\[\left(
\begin{array}{cc}
n=1 & 2^n+3^n= 5 \\
n= 2 & 2^n+3^n= 13 \\
n= 3 & 2^n+3^n= 35 \\
n= 4 & 2^n+3^n= 97 \\
n= 5 & 2^n+3^n= 275 \\
n= 6 & 2^n+3^n= 793 \\
\end{array}
\right)
\]

and
\[

6^3=216\]
So there is no such n