Precalculus Examples

$\log (8 x) - 3 \log (2) - \log (x)$

Step 1

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

$\log (\frac{8 x}{x}) - 3 \log (2)$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $x$ .

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Step 2.1.1

Cancel the common factor.

$\log (\frac{8 x}{x}) - 3 \log (2)$

Step 2.1.2

Divide $8$ by $1$ .

$\log (8) - 3 \log (2)$

Step 2.2

Simplify $- 3 \log (2)$ by moving $3$ inside the logarithm.

$\log (8) - \log (2^{3})$

Step 2.3

Raise $2$ to the power of $3$ .

$\log (8) - \log (8)$

Step 3

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

$\log (\frac{8}{8})$

Step 4

Divide $8$ by $8$ .

$\log (1)$

Step 5

Logarithm base $10$ of $1$ is $0$ .

$0$