Question

Solve 9^2x+3=27^2x Need help please.

Answer 1

`\bf 9^(2x+3)=27^(2x)\qquad \begin{cases} 9=3^2\\ 27=3^3 \end{cases}\implies (3^2)^(2x+3)=(3^3)^(2x) \\\\\\ 3^(2(2x+3))=3^(3(2x))\implies 3^(4x+6)=3^(6x)\impliedby \begin{array}{llll} \textit{base is the same, therefore,}\\ \textit{the exponents must}\\ \textit{ also be the same} \end{array} \\\\\\ 4x+6=6x\implies 6=2x\implies \cfrac{6}{2}=x\implies 3=x`