Question

9^x = 27^2x+8

Solve

Answer 1

`9^x~~ = ~~27^(2x+8) ~~ \begin{cases} 9=3^2\\ 27=3^3 \end{cases}\implies (3^2)^x~~ = ~~(3^3)^(2x+8) \\\\\\ \stackrel{\textit{same base, exponents must be equal}}{3^(2(x))~~ = ~~3^(3(2x+8))\implies 2(x)=3(2x+8)}\implies 2x=6x+24 \\\\\\ 0=4x+24\implies -24=4x\implies \cfrac{-24}{4}=x\implies -6=x`