Calculus Examples

$\log_{5} (x - 7) = 2$

Step 1

Rewrite $\log_{5} (x - 7) = 2$ 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 $b^{y} = x$ .

$5^{2} = x - 7$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $x - 7 = 5^{2}$ .

$x - 7 = 5^{2}$

Step 2.2

Raise $5$ to the power of $2$ .

$x - 7 = 25$

Step 2.3

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

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Step 2.3.1

Add $7$ to both sides of the equation.

$x = 25 + 7$

Step 2.3.2

Add $25$ and $7$ .

$x = 32$