Solve for x log base x of 27=3/4

$\log_{x} (27) = \frac{3}{4}$

Rewrite $\log_{x} (27) = \frac{3}{4}$ 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 $b^{y} = x$ .

$x^{\frac{3}{4}} = 27$

Solve for $x$ .

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

${(x^{\frac{3}{4}})}^{\frac{4}{3}} = 27^{\frac{4}{3}}$

Simplify the exponent.

Simplify the left side.

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

Multiply the exponents in ${(x^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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

$x^{\frac{3}{4} \cdot \frac{4}{3}} = 27^{\frac{4}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{3}{4} \cdot \frac{4}{3}} = 27^{\frac{4}{3}}$

Rewrite the expression.

$x^{\frac{1}{4} \cdot 4} = 27^{\frac{4}{3}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$x^{\frac{1}{4} \cdot 4} = 27^{\frac{4}{3}}$

Rewrite the expression.

$x^{1} = 27^{\frac{4}{3}}$

Simplify.

$x = 27^{\frac{4}{3}}$

Simplify the right side.

Simplify $27^{\frac{4}{3}}$ .

Simplify the expression.

Rewrite $27$ as $3^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 3^{4}$

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

$x = 81$

Solve for x log base x of 27=3/4

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