Solve for x log base 16 of x=3/2

$\log_{16} (x) = \frac{3}{2}$

Rewrite $\log_{16} (x) = \frac{3}{2}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$16^{\frac{3}{2}} = x$

Solve for $x$ .

Rewrite the equation as $x = 16^{\frac{3}{2}}$ .

$x = 16^{\frac{3}{2}}$

Simplify $16^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $16$ as $4^{2}$ .

$x = {(4^{2})}^{\frac{3}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = 4^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = 4^{2 (\frac{3}{2})}$

Rewrite the expression.

$x = 4^{3}$

Raise $4$ to the power of $3$ .

$x = 64$

Solve for x log base 16 of x=3/2

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