Solve for x log base 81 of x=1/2

$\log_{81} (x) = \frac{1}{2}$

Step 1

Rewrite $\log_{81} (x) = \frac{1}{2}$ 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 $b^{y} = x$ .

$81^{\frac{1}{2}} = x$

Step 2

Solve for $x$ .

Rewrite the equation as $x = 81^{\frac{1}{2}}$ .

$x = 81^{\frac{1}{2}}$

Simplify $81^{\frac{1}{2}}$ .

Simplify the expression.

Rewrite $81$ as $9^{2}$ .

$x = {(9^{2})}^{\frac{1}{2}}$

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

$x = 9^{2 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = 9^{2 (\frac{1}{2})}$

Rewrite the expression.

$x = 9^{1}$

Evaluate the exponent.

$x = 9$

Solve for x log base 81 of x=1/2

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