Question

If $2^{x+1}=3^{1-x}$ then find the value of $x$ ?

Answer 1

$2^x\cdot 2=\frac{3}{3^x}$
$⟹2^x\cdot 3^x=\frac{3}{2}$
$⟹6^x=\frac{3}{2}$
$⟹x={\log }_6\left(\frac{3}{2}\right)$