Question

Solve for $x$ .

$\left[{12}^{8x}\times 12\right]÷{12}^7=20736$

Answer 1

Given that , $\left[{12}^{8x}\times 12\right]÷{12}^7=20736$

$\Rightarrow \frac{{12}^{8x}\times 12}{{12}^7}=20736$

$\Rightarrow {12}^{8x}\times 12\times {12}^{-7}=20736$

$\Rightarrow {12}^{8x+1-7}={12}^4$

$\Rightarrow {12}^{8x-6}={12}^4$ [ using laws of exponent : $a^{-n}=\frac{1}{a^n}$ , $a^n=a^m\Rightarrow m=n$ and $a^n\times a^m=a^{m+n}$ ]

$\Rightarrow 8x-6=4$

$\Rightarrow 8x=4+6$

$\Rightarrow 8x=10$

$\Rightarrow x=\frac{10}{8}$

$\Rightarrow x=\frac{5}{4}$

Hence, the required value of $x$ is $\frac{5}{4}$.