Precalculus Examples

$4 \log (x) - 2 (\log (y) + \log (z))$

Step 1

Simplify each term.

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Step 1.1

Simplify $4 \log (x)$ by moving $4$ inside the logarithm.

$\log (x^{4}) - 2 (\log (y) + \log (z))$

Step 1.2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x^{4}) - 2 \log (y z)$

Step 1.3

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

$\log (x^{4}) - \log ({(y z)}^{2})$

Step 1.4

Apply the product rule to $y z$ .

$\log (x^{4}) - \log (y^{2} z^{2})$

Step 2

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

$\log (\frac{x^{4}}{y^{2} z^{2}})$