Algebra Examples

{log}_{x} (32) = 5

$\log_{x} (32) = 5$

Step 1

Rewrite

{log}_{x} (32) = 5

$\log_{x} (32) = 5$ in exponential form using the definition of a logarithm. If

x

$x$ and

b

$b$ are positive real numbers and

b \neq 1

$b \neq 1$ , then

{log}_{b} (x) = y

$\log_{b} (x) = y$ is equivalent to

b^{y} = x

$b^{y} = x$ .

x^{5} = 32

$x^{5} = 32$

Step 2

Solve for

x

$x$ .

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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]{32}

$x = \sqrt[5]{32}$

Step 2.2

Simplify

\sqrt[5]{32}

$\sqrt[5]{32}$ .

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Step 2.2.1

Rewrite

32

$32$ as

2^{5}

$2^{5}$ .

x = \sqrt[5]{2^{5}}

$x = \sqrt[5]{2^{5}}$

Step 2.2.2

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

x = 2

$x = 2$

x = 2

$x = 2$

x = 2

$x = 2$