Solve for x log base 125 of x=2/3

$\log_{125} (x) = \frac{2}{3}$

Step 1

Rewrite $\log_{125} (x) = \frac{2}{3}$ 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 $b^{y} = x$ .

$125^{\frac{2}{3}} = x$

Step 2

Solve for $x$ .

Rewrite the equation as $x = 125^{\frac{2}{3}}$ .

$x = 125^{\frac{2}{3}}$

Simplify $125^{\frac{2}{3}}$ .

Simplify the expression.

Rewrite $125$ as $5^{3}$ .

$x = {(5^{3})}^{\frac{2}{3}}$

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

$x = 5^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x = 5^{3 (\frac{2}{3})}$

Rewrite the expression.

$x = 5^{2}$

Raise $5$ to the power of $2$ .

$x = 25$

Solve for x log base 125 of x=2/3

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