Precalculus Examples

$- 3 \log_{4} (4 x)$

Step 1

Simplify $- 3 \log_{4} (4 x)$ by moving $3$ inside the logarithm.

$- \log_{4} ({(4 x)}^{3})$

Step 2

Apply the product rule to $4 x$ .

$- \log_{4} (4^{3} x^{3})$

Step 3

Rewrite $\log_{4} (4^{3} x^{3})$ as $\log_{4} (4^{3}) + \log_{4} (x^{3})$ .

$- (\log_{4} (4^{3}) + \log_{4} (x^{3}))$

Step 4

Use logarithm rules to move $3$ out of the exponent.

$- (3 \log_{4} (4) + \log_{4} (x^{3}))$

Step 5

Logarithm base $4$ of $4$ is $1$ .

$- (3 \cdot 1 + \log_{4} (x^{3}))$

Step 6

Multiply $3$ by $1$ .

$- (3 + \log_{4} (x^{3}))$

Step 7

Apply the distributive property.

$- 1 \cdot 3 - \log_{4} (x^{3})$

Step 8

Multiply $- 1$ by $3$ .

$- 3 - \log_{4} (x^{3})$