Precalculus Examples

$\ln (x - 4) = 0$

Step 1

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (x - 4)} = e^{0}$

Step 2

Rewrite $\ln (x - 4) = 0$ 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 $b^{y} = x$ .

$e^{0} = x - 4$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $x - 4 = e^{0}$ .

$x - 4 = e^{0}$

Step 3.2

Anything raised to $0$ is $1$ .

$x - 4 = 1$

Step 3.3

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

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Step 3.3.1

Add $4$ to both sides of the equation.

$x = 1 + 4$

Step 3.3.2

Add $1$ and $4$ .

$x = 5$