Solve for m log base m of 81=4

$\log_{m} (81) = 4$

Step 1

Rewrite $\log_{m} (81) = 4$ 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 $b^{y} = x$ .

$m^{4} = 81$

Step 2

Solve for $m$ .

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

$m = \pm \sqrt[4]{81}$

Simplify $\pm \sqrt[4]{81}$ .

Rewrite $81$ as $3^{4}$ .

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

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

$m = \pm 3$

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

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

$m = 3$

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

$m = - 3$

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

$m = 3, - 3$

Step 3

Exclude the solutions that do not make $\log_{m} (81) = 4$ true.

$m = 3$

Solve for m log base m of 81=4

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