# How do you condense lnx-3ln(x+1)?

Apr 10, 2018

$\ln \frac{x}{x + 1} ^ 3$

#### Explanation:

We have an expression:

$\ln x - 3 \ln \left(x + 1\right)$

We use two properties of logarithms:

$a \log b \equiv \log {b}^{a}$ and $\log a - \log b \equiv \log \left(\frac{a}{b}\right)$

Applying the first property we can write the expression as:

$\ln x - \ln {\left(x + 1\right)}^{3}$

And applying the second property we can write the expression as:

$\ln \left(\frac{x}{x + 1} ^ 3\right)$