Precalculus Examples

$0 = \ln (x + 3)$

Step 1

Rewrite the equation as $\ln (x + 3) = 0$ .

$\ln (x + 3) = 0$

Step 2

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

$e^{\ln (x + 3)} = e^{0}$

Step 3

Rewrite $\ln (x + 3) = 0$ 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 $b^{y} = x$ .

$e^{0} = x + 3$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

Rewrite the equation as $x + 3 = e^{0}$ .

$x + 3 = e^{0}$

Step 4.2

Anything raised to $0$ is $1$ .

$x + 3 = 1$

Step 4.3

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

Tap for more steps...

Step 4.3.1

Subtract $3$ from both sides of the equation.

$x = 1 - 3$

Step 4.3.2

Subtract $3$ from $1$ .

$x = - 2$