Question

If

$2^3{\frac{2}{3}}^x=8\frac{8}{27}$

Find the value of $x$?

Answer 1

$2^3{\left(\frac{2}{3}\right)}^2=8\frac{8}{27}$

$\therefore 8{\left(\frac{2}{3}\right)}^x=8\frac{8}{27}$

$\therefore {\left(\frac{2}{3}\right)}^x=\frac{8}{27}$ ....... $\left(1\right)$

Now $\frac{8}{27}={\left(\frac{2}{3}\right)}^3$

$\therefore$ from $\left(1\right)$ & $\left(2\right)$

$x=3$