Question

Find the value of $x$ for the given equation ${\left(\frac{3}{4}\right)}^3{\left(\frac{4}{3}\right)}^{-7}=\left(\frac{3}{4}\right)2x$

Answer 1

We have,

${\left(\frac{3}{4}\right)}^3\times {\left(\frac{4}{3}\right)}^{-7}=\left(\frac{3}{4}\right)\times 2x$

${\left(\frac{3}{4}\right)}^3\times {\left(\frac{3}{4}\right)}^7=\left(\frac{3}{4}\right)\times 2x$

${\left(\frac{3}{4}\right)}^3\times {\left(\frac{3}{4}\right)}^6=2x$

${\left(\frac{3}{4}\right)}^9=2x$

$x=\frac{1}{2}{\left(\frac{3}{4}\right)}^9$

Hence, the value of $x$ is $\frac{1}{2}{\left(\frac{3}{4}\right)}^9$.