Question

Solve for x:

$9\times {81}^x={27}^{2-x}$

Answer 1

Given $9\times {81}^x={27}^{2-x}$

$⟹3^2\times (3^4{)}^x=(3^3{)}^{2-x}$

$⟹3^2\times 3^{4x}=3^{6-3x}$

$⟹2+4x=6-3x$

$⟹7x=4⟹x=\frac{4}{7}$