Precalculus Examples

$\log_{3} (x - 2) = 1$

Step 1

Rewrite $\log_{3} (x - 2) = 1$ 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 $b^{y} = x$ .

$3^{1} = x - 2$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $x - 2 = 3^{1}$ .

$x - 2 = 3$

Step 2.2

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

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Step 2.2.1

Add $2$ to both sides of the equation.

$x = 3 + 2$

Step 2.2.2

Add $3$ and $2$ .

$x = 5$