Trigonometry Examples

$4 = \log_{m} (625)$

Step 1

Rewrite the equation as $\log_{m} (625) = 4$ .

$\log_{m} (625) = 4$

Step 2

Rewrite $\log_{m} (625) = 4$ 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 $b^{y} = x$ .

$m^{4} = 625$

Step 3

Solve for $m$ .

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Step 3.1

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

$m = \pm \sqrt[4]{625}$

Step 3.2

Simplify $\pm \sqrt[4]{625}$ .

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Step 3.2.1

Rewrite $625$ as $5^{4}$ .

$m = \pm \sqrt[4]{5^{4}}$

Step 3.2.2

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

$m = \pm 5$

Step 3.3

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

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Step 3.3.1

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

$m = 5$

Step 3.3.2

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

$m = - 5$

Step 3.3.3

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

$m = 5, - 5$

Step 4

Exclude the solutions that do not make $4 = \log_{m} (625)$ true.

$m = 5$