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

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Answer 1 · 2018-04-10T12:35:38

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

We have an expression:

$ln x - 3 ln (x + 1)$ $ln x - 3ln(x+1)$

We use two properties of logarithms:

$a log b \equiv {log b}^{a}$ $alogb -= logb^a$ and $log a - log b \equiv log (\frac{a}{b})$ $log a-logb -= log(a/b)$

Applying the first property we can write the expression as:

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

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

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

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