Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[{2}^{x\times \frac{1}{2}}=32then\]
Simplify \(x\times \frac{1}{2}\) to \(\frac{x}{2}\).
\[{2}^{\frac{x}{2}}=32then\]
Regroup terms.
\[{2}^{\frac{x}{2}}=32ethn\]
Use Definition of Common Logarithm: \({b}^{a}=x\) if and only if \(log_b(x)=a\).
\[\frac{x}{2}=\log_{2}{(32ethn)}\]
Multiply both sides by \(2\).
\[x=\log_{2}{(32ethn)}\times 2\]
Use Power Rule: \(\log_{b}{{x}^{c}}=c\log_{b}{x}\).
\[x=\log_{2}{{(32ethn)}^{2}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[x=\log_{2}{({32}^{2}{e}^{2}{t}^{2}{h}^{2}{n}^{2})}\]
Simplify \({32}^{2}\) to \(1024\).
\[x=\log_{2}{(1024{e}^{2}{t}^{2}{h}^{2}{n}^{2})}\]
x=log(2,1024*e^2*t^2*h^2*n^2)
