Question

solve 27^x=9^(2x-7), show work and explain steps

Answer 1

\(\large {
27^x=9^{2x-7}\qquad
\begin{cases}
27\to 3\cdot 3\cdot 3\to 3^3
\\ \quad \\
9\to 3\cdot 3\to 3^2
\end{cases}\qquad thus
\\ \quad \\
27^x=9^{2x-7}\implies (3^3)^x=(3^2)^{2x-7}\implies
3^{{\color{blue}{ 3x}}}=3^{{\color{blue}{ 2(2x-7)}}}
}\)