To determine:

To solve \(\displaystyle{32}^{{x}}={8}\) by expressing each side as a power of the same base and then equating exponents.

Calculation:

We know, \(\displaystyle{32}={2}\times{2}\times{2}\times{2}\times{2}\)

\(\displaystyle\Rightarrow{32}={2}^{{5}}\)

Also, \(\displaystyle{8}={2}\times{2}\times{2}\)

\(\displaystyle\Rightarrow{8}={2}^{{3}}\)

Plugging these values in the given equation, we get,

\(\displaystyle{\left({2}^{{5}}\right)}^{{x}}={2}^{{3}}\)

\(\displaystyle\Rightarrow{2}^{{{5}{x}}}={2}^{{3}}\)

If base are same the equating powers, we get,

\(\displaystyle{5}{x}={3}\)

\(\displaystyle\Rightarrow{x}={\frac{{{3}}}{{{5}}}}\)

Hence, \(\displaystyle{x}={\frac{{{3}}}{{{5}}}}\) is the solution of given equation.

To solve \(\displaystyle{32}^{{x}}={8}\) by expressing each side as a power of the same base and then equating exponents.

Calculation:

We know, \(\displaystyle{32}={2}\times{2}\times{2}\times{2}\times{2}\)

\(\displaystyle\Rightarrow{32}={2}^{{5}}\)

Also, \(\displaystyle{8}={2}\times{2}\times{2}\)

\(\displaystyle\Rightarrow{8}={2}^{{3}}\)

Plugging these values in the given equation, we get,

\(\displaystyle{\left({2}^{{5}}\right)}^{{x}}={2}^{{3}}\)

\(\displaystyle\Rightarrow{2}^{{{5}{x}}}={2}^{{3}}\)

If base are same the equating powers, we get,

\(\displaystyle{5}{x}={3}\)

\(\displaystyle\Rightarrow{x}={\frac{{{3}}}{{{5}}}}\)

Hence, \(\displaystyle{x}={\frac{{{3}}}{{{5}}}}\) is the solution of given equation.