Precalculus Examples

$\log_{x} (1024) = 5$

Step 1

Rewrite $\log_{x} (1024) = 5$ 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 $b^{y} = x$ .

$x^{5} = 1024$

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.

$x = \sqrt[5]{1024}$

Step 2.2

Simplify $\sqrt[5]{1024}$ .

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Step 2.2.1

Rewrite $1024$ as $4^{5}$ .

$x = \sqrt[5]{4^{5}}$

Step 2.2.2

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

$x = 4$