Precalculus Examples

$\log (\frac{x^{4} y}{w z^{3}})$

Step 1

Rewrite $\log (\frac{x^{4} y}{w z^{3}})$ as $\log (x^{4} y) - \log (w z^{3})$ .

$\log (x^{4} y) - \log (w z^{3})$

Step 2

Rewrite $\log (x^{4} y)$ as $\log (x^{4}) + \log (y)$ .

$\log (x^{4}) + \log (y) - \log (w z^{3})$

Step 3

Expand $\log (x^{4})$ by moving $4$ outside the logarithm.

$4 \log (x) + \log (y) - \log (w z^{3})$

Step 4

Rewrite $\log (w z^{3})$ as $\log (w) + \log (z^{3})$ .

$4 \log (x) + \log (y) - (\log (w) + \log (z^{3}))$

Step 5

Expand $\log (z^{3})$ by moving $3$ outside the logarithm.

$4 \log (x) + \log (y) - (\log (w) + 3 \log (z))$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Apply the distributive property.

$4 \log (x) + \log (y) - \log (w) - (3 \log (z))$

Step 6.2

Multiply $3$ by $- 1$ .

$4 \log (x) + \log (y) - \log (w) - 3 \log (z)$