Algebra Examples

$\log_{3} (x + 4) = 2$

Step 1

Rewrite $\log_{3} (x + 4) = 2$ 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 $b^{y} = x$ .

$3^{2} = x + 4$

Step 2

Solve for $x$ .

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Rewrite the equation as $x + 4 = 3^{2}$ .

$x + 4 = 3^{2}$

Raise $3$ to the power of $2$ .

$x + 4 = 9$

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

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Subtract $4$ from both sides of the equation.

$x = 9 - 4$

Subtract $4$ from $9$ .

$x = 5$