Question

Solve for $x:$

$9^{x+2}=720+9^x$

Answer 1

Step : Finding teh value of $x$

$9^{x+2}=720+9^x$

$9^x\times 9^2-9^x=720(\therefore a^{m+n}=a^m\times a^n)$

$\Rightarrow 9^x\times 81-9^x=720$

$\Rightarrow (81-1){.9}^x=720$

$\Rightarrow {80.9}^x=720$

$\Rightarrow 9^x=\frac{720}{80}=9$

$9^x=9^1$

$\therefore x=1$

Hence, the value of $x$ is 1.