Basic Math Examples

$\log (q^{2} + 1) = 1$

Step 1

Rewrite $\log (q^{2} + 1) = 1$ 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 $b^{y} = x$ .

$10^{1} = q^{2} + 1$

Step 2

Solve for $q$ .

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Step 2.1

Rewrite the equation as $q^{2} + 1 = 10^{1}$ .

$q^{2} + 1 = 10$

Step 2.2

Move all terms not containing $q$ to the right side of the equation.

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Step 2.2.1

Subtract $1$ from both sides of the equation.

$q^{2} = 10 - 1$

Step 2.2.2

Subtract $1$ from $10$ .

$q^{2} = 9$

Step 2.3

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

$q = \pm \sqrt{9}$

Step 2.4

Simplify $\pm \sqrt{9}$ .

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Step 2.4.1

Rewrite $9$ as $3^{2}$ .

$q = \pm \sqrt{3^{2}}$

Step 2.4.2

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

$q = \pm 3$

Step 2.5

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

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Step 2.5.1

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

$q = 3$

Step 2.5.2

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

$q = - 3$

Step 2.5.3

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

$q = 3, - 3$