Algebra Examples

Simplify $2 \ln (x + 2) - \ln (x + 2) - \ln (2) - 3$

Step 1

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

$\ln ({(x + 2)}^{2}) - \ln (x + 2) - \ln (2) - 3$

Step 2

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

$\ln (\frac{{(x + 2)}^{2}}{x + 2}) - \ln (2) - 3$

Step 3

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

$\ln (\frac{\frac{{(x + 2)}^{2}}{x + 2}}{2}) - 3$

Step 4

Cancel the common factor of ${(x + 2)}^{2}$ and $x + 2$ .

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Step 4.1

Factor $x + 2$ out of ${(x + 2)}^{2}$ .

$\ln (\frac{\frac{(x + 2) (x + 2)}{x + 2}}{2}) - 3$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\ln (\frac{\frac{(x + 2) (x + 2)}{(x + 2) \cdot 1}}{2}) - 3$

Step 4.2.2

Cancel the common factor.

$\ln (\frac{\frac{(x + 2) (x + 2)}{(x + 2) \cdot 1}}{2}) - 3$

Step 4.2.3

Rewrite the expression.

$\ln (\frac{\frac{x + 2}{1}}{2}) - 3$

Step 4.2.4

Divide $x + 2$ by $1$ .

$\ln (\frac{x + 2}{2}) - 3$