Question

If ${\left(\frac{2}{5}\right)}^x={\left(\frac{5}{2}\right)}^x\times \left(\frac{4}{25}\right)$. Find the value of $x$.

Answer 1

${\left(\frac{2}{5}\right)}^x={\left(\frac{5}{2}\right)}^x\times \left(\frac{4}{25}\right)$

$(\frac{2}{5}{)}^x=(\frac{2}{5}{)}^{-x}\times (\frac{2}{5}{)}^2$

$(\frac{2}{5}{)}^x=(\frac{2}{5}{)}^{2-x}$

$⟹x=2-x$

$⟹2x=2$

$⟹x=1$