Trigonometry Examples

$\ln (- 2 x - 2) - \ln (x + 6) = \ln (- 11 x - 18)$

Step 1

Simplify $\ln (- 2 x - 2) - \ln (x + 6)$ .

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Step 1.1

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

$\ln (\frac{- 2 x - 2}{x + 6}) = \ln (- 11 x - 18)$

Step 1.2

Factor $2$ out of $- 2 x - 2$ .

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Step 1.2.1

Factor $2$ out of $- 2 x$ .

$\ln (\frac{2 (- x) - 2}{x + 6}) = \ln (- 11 x - 18)$

Step 1.2.2

Factor $2$ out of $- 2$ .

$\ln (\frac{2 (- x) + 2 (- 1)}{x + 6}) = \ln (- 11 x - 18)$

Step 1.2.3

Factor $2$ out of $2 (- x) + 2 (- 1)$ .

$\ln (\frac{2 (- x - 1)}{x + 6}) = \ln (- 11 x - 18)$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 5.79032831$

Step 3