Trigonometry Examples

$\ln (x + 4) - \ln (18) = \ln (5)$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{x + 4}{18}) = \ln (5)$

Step 2

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

$\frac{x + 4}{18} = 5$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides of the equation by $18$ .

$18 \frac{x + 4}{18} = 18 \cdot 5$

Step 3.2

Simplify both sides of the equation.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $18$ .

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Step 3.2.1.1.1

Cancel the common factor.

$18 \frac{x + 4}{18} = 18 \cdot 5$

Step 3.2.1.1.2

Rewrite the expression.

$x + 4 = 18 \cdot 5$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $18$ by $5$ .

$x + 4 = 90$

Step 3.3

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

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Step 3.3.1

Subtract $4$ from both sides of the equation.

$x = 90 - 4$

Step 3.3.2

Subtract $4$ from $90$ .

$x = 86$