Precalculus Examples

$2 \ln (1) + 2 \ln (5) = \ln (x + 3)$

Step 1

Rewrite the equation as $\ln (x + 3) = 2 \ln (1) + 2 \ln (5)$ .

$\ln (x + 3) = 2 \ln (1) + 2 \ln (5)$

Step 2

Simplify the right side.

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Step 2.1

Simplify $2 \ln (1) + 2 \ln (5)$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

The natural logarithm of $1$ is $0$ .

$\ln (x + 3) = 2 \cdot 0 + 2 \ln (5)$

Step 2.1.1.2

Multiply $2$ by $0$ .

$\ln (x + 3) = 0 + 2 \ln (5)$

Step 2.1.1.3

Simplify $2 \ln (5)$ by moving $2$ inside the logarithm.

$\ln (x + 3) = 0 + \ln (5^{2})$

Step 2.1.1.4

Raise $5$ to the power of $2$ .

$\ln (x + 3) = 0 + \ln (25)$

Step 2.1.2

Add $0$ and $\ln (25)$ .

$\ln (x + 3) = \ln (25)$

Step 3

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$x + 3 = 25$

Step 4

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

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Step 4.1

Subtract $3$ from both sides of the equation.

$x = 25 - 3$

Step 4.2

Subtract $3$ from $25$ .

$x = 22$