Solve for x log base 8 of x=1/3

$\log_{8} (x) = \frac{1}{3}$

Rewrite $\log_{8} (x) = \frac{1}{3}$ 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 $b^{y} = x$ .

$8^{\frac{1}{3}} = x$

Solve for $x$ .

Rewrite the equation as $x = 8^{\frac{1}{3}}$ .

$x = 8^{\frac{1}{3}}$

Simplify $8^{\frac{1}{3}}$ .

Simplify the expression.

Rewrite $8$ as $2^{3}$ .

$x = {(2^{3})}^{\frac{1}{3}}$

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

$x = 2^{3 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x = 2^{3 (\frac{1}{3})}$

Rewrite the expression.

$x = 2^{1}$

Evaluate the exponent.

$x = 2$

Solve for x log base 8 of x=1/3

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