Question

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

Answer 1

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