Solve for x log base x of 64=3/4

$\log_{x} (64) = \frac{3}{4}$

Rewrite $\log_{x} (64) = \frac{3}{4}$ 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 $b^{y} = x$ .

$x^{\frac{3}{4}} = 64$

Solve for $x$

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Remove parentheses.

$x^{\frac{3}{4}} = 64$

Raise each side of the equation to the $\frac{4}{3}$ power to eliminate the fractional exponent on the left side.

${(x^{\frac{3}{4}})}^{\frac{4}{3}} = {(64)}^{\frac{4}{3}}$

Simplify ${(64)}^{\frac{4}{3}}$ .

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Simplify the expression.

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Rewrite $64$ as $4^{3}$ .

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

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

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

Cancel the common factor of $3$ .

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Cancel the common factor.

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

Rewrite the expression.

$x = 4^{4}$

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

$x = 256$

Solve for x log base x of 64=3/4