Algebra Examples

$\log_{5} (x + 30) = 3$

Step 1

Rewrite $\log_{5} (x + 30) = 3$ 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 $b^{y} = x$ .

$5^{3} = x + 30$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $x + 30 = 5^{3}$ .

$x + 30 = 5^{3}$

Step 2.2

Raise $5$ to the power of $3$ .

$x + 30 = 125$

Step 2.3

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

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Step 2.3.1

Subtract $30$ from both sides of the equation.

$x = 125 - 30$

Step 2.3.2

Subtract $30$ from $125$ .

$x = 95$