Solve for x 2 log of x = log of 81

$2 \log (x) = \log (81)$

Simplify $2 \log (x)$ by moving $2$ inside the logarithm.

$\log (x^{2}) = \log (81)$

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$x^{2} = 81$

Solve for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{81}$

Simplify $\pm \sqrt{81}$ .

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

$x = \pm \sqrt{9^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 9$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 9$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 9$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 9, - 9$

Exclude the solutions that do not make $2 \log (x) = \log (81)$ true.

$x = 9$