Precalculus Examples

$8 + \ln (27 x) - 26 - 2 \ln (x)$

Step 1

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

$8 + \ln (27 x) - 26 - \ln (x^{2})$

Step 2

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

$8 + \ln (\frac{27 x}{x^{2}}) - 26$

Step 3

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

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Step 3.1

Factor $x$ out of $27 x$ .

$8 + \ln (\frac{x \cdot 27}{x^{2}}) - 26$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $x^{2}$ .

$8 + \ln (\frac{x \cdot 27}{x \cdot x}) - 26$

Step 3.2.2

Cancel the common factor.

$8 + \ln (\frac{x \cdot 27}{x \cdot x}) - 26$

Step 3.2.3

Rewrite the expression.

$8 + \ln (\frac{27}{x}) - 26$

Step 4

Subtract $26$ from $8$ .

$- 18 + \ln (\frac{27}{x})$