Precalculus Examples

$\log ({(x)}^{4}) = \log ({(256)}^{3})$

Step 1

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

$x^{4} = 256^{3}$

Step 2

Solve for $x$ .

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Step 2.1

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

$x = \pm \sqrt[4]{256^{3}}$

Step 2.2

Simplify $\pm \sqrt[4]{256^{3}}$ .

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Step 2.2.1

Raise $256$ to the power of $3$ .

$x = \pm \sqrt[4]{16777216}$

Step 2.2.2

Rewrite $16777216$ as $64^{4}$ .

$x = \pm \sqrt[4]{64^{4}}$

Step 2.2.3

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

$x = \pm 64$

Step 2.3

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

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Step 2.3.1

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

$x = 64$

Step 2.3.2

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

$x = - 64$

Step 2.3.3

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

$x = 64, - 64$