Precalculus Examples

$\log_{x} (16) = 4$

Step 1

Rewrite $\log_{x} (16) = 4$ 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 $b^{y} = x$ .

$x^{4} = 16$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

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

$x = \pm \sqrt[4]{16}$

Step 2.2

Simplify $\pm \sqrt[4]{16}$ .

Tap for more steps...

Step 2.2.1

Rewrite $16$ as $2^{4}$ .

$x = \pm \sqrt[4]{2^{4}}$

Step 2.2.2

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

$x = \pm 2$

Step 2.3

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

Tap for more steps...

Step 2.3.1

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

$x = 2$

Step 2.3.2

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

$x = - 2$

Step 2.3.3

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

$x = 2, - 2$

Step 3

Exclude the solutions that do not make $\log_{x} (16) = 4$ true.

$x = 2$