Precalculus Examples

$\log (\frac{1}{x}) + 4 \log (x)$

Step 1

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

$\log (\frac{1}{x}) + \log (x^{4})$

Step 2

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

$\log (\frac{1}{x} x^{4})$

Step 3

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.1

Factor $x$ out of $x^{4}$ .

$\log (\frac{1}{x} (x \cdot x^{3}))$

Step 3.2

Cancel the common factor.

$\log (\frac{1}{x} (x \cdot x^{3}))$

Step 3.3

Rewrite the expression.

$\log (x^{3})$