Question

If $9^x\times 3^2\times {\left(3^{\frac{-x}{2}}\right)}^{-2}=\frac{1}{27}$, find $x$.

Answer 1

The given equation is :

$9^x\times 3^2\times {\left(3^{\frac{-x}{2}}\right)}^{-2}=\frac{1}{27}$

It can be written as:

$3^{2x}\times 3^2\times 3^x=3^{-3}$

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

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

Now,since the bases are same,then comparing the powers,we get $3x+2=-3$

$x=\frac{-5}{3}$