# How do you condense 3 log + 4 log y - 2 log z?

Dec 17, 2016

$\log \left(\frac{{x}^{3} {y}^{4}}{z} ^ 2\right)$

#### Explanation:

Condense $3 \log x + 4 \log y - 2 \log z$

Note: I assumed there was a typo in the question and added an $x$.

First, use the log rule $a \log x = \log {x}^{a}$

$\log {x}^{3} + \log {y}^{4} - \log {z}^{2}$

Next, use the log rules

$\log a + \log b = \log \left(a b\right)$ and $\log a - \log b = \log \left(\frac{a}{b}\right)$

There is a somewhat silly expression for this rule: in the land of logs, addition is multiplication and subtraction is division.

$\log \left(\frac{{x}^{3} {y}^{4}}{z} ^ 2\right)$