Question

If $2^x\times 4^x={\left(8\right)}^{\frac{1}{3}}\times {\left(32\right)}^{\frac{1}{5}}$ then, find the value of $x$

Answer 1

We have,

$2^x\times 4^x={\left(8\right)}^{\frac{1}{3}}\times {\left(32\right)}^{\frac{1}{5}}$

$2^x\times (2^2{)}^x={\left(\right(2^3\left)\right)}^{\frac{1}{3}}\times {\left(2^5\right)}^{\frac{1}{5}}$

$2^x\times 2^{2x}=2\times 2$

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

$2^{3x}=2^2$

On comparing both sides, we get

$3x=2$

$x=\frac{2}{3}$

Hence, this is the answer.