Basic Math Examples

\log_{b} (144) = 2

$\log_{b} (144) = 2$

Step 1

Rewrite

\log_{b} (144) = 2

$\log_{b} (144) = 2$ 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

$b^{y} = x$ .

b^{2} = 144

$b^{2} = 144$

Step 2

Solve for

b

$b$ .

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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.

b = \pm \sqrt{144}

$b = \pm \sqrt{144}$

Step 2.2

Simplify

\pm \sqrt{144}

$\pm \sqrt{144}$ .

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Step 2.2.1

Rewrite

144

$144$ as

12^{2}

$12^{2}$ .

b = \pm \sqrt{12^{2}}

$b = \pm \sqrt{12^{2}}$

Step 2.2.2

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

b = \pm 12

$b = \pm 12$

b = \pm 12

$b = \pm 12$

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

$\pm$ to find the first solution.

b = 12

$b = 12$

Step 2.3.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

b = - 12

$b = - 12$

Step 2.3.3

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

b = 12, - 12

$b = 12, - 12$

b = 12, - 12

$b = 12, - 12$

b = 12, - 12

$b = 12, - 12$

Step 3

Exclude the solutions that do not make

\log_{b} (144) = 2

$\log_{b} (144) = 2$ true.

b = 12

$b = 12$