Algebra Examples

$\log_{4} (x - 2) = 2$

Step 1

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

$4^{2} = x - 2$

Step 2

Solve for $x$ .

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

$x - 2 = 4^{2}$

Raise $4$ to the power of $2$ .

$x - 2 = 16$

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

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Add $2$ to both sides of the equation.

$x = 16 + 2$

Add $16$ and $2$ .

$x = 18$