Precalculus Examples

$\log_{4} (x - 3) = 3$

Step 1

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

$4^{3} = x - 3$

Step 2

Solve for $x$ .

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Step 2.1

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

$x - 3 = 4^{3}$

Step 2.2

Raise $4$ to the power of $3$ .

$x - 3 = 64$

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 $3$ to both sides of the equation.

$x = 64 + 3$

Step 2.3.2

Add $64$ and $3$ .

$x = 67$