Precalculus Examples

$\log (x - 4) = 3$

Step 1

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

$10^{3} = x - 4$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $x - 4 = 10^{3}$ .

$x - 4 = 10^{3}$

Step 2.2

Raise $10$ to the power of $3$ .

$x - 4 = 1000$

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 $4$ to both sides of the equation.

$x = 1000 + 4$

Step 2.3.2

Add $1000$ and $4$ .

$x = 1004$