corniness9a

## Answered question

2022-10-08

Express the given expression as a single logarithm
Express
$2\mathrm{ln}\left(2-x\right)+3\mathrm{ln}\left({x}^{2}-5\right)$
as a single logarithm.
Can anyone help me with this question? Thanks

### Answer & Explanation

Olleschauvh

Beginner2022-10-09Added 4 answers

Using properties of logarithms we have
$a\mathrm{ln}b=\mathrm{ln}{b}^{a}$
and
$\mathrm{ln}x+\mathrm{ln}y=\mathrm{ln}xy$
We get
$\begin{array}{rl}2\mathrm{ln}\left(2-x\right)+3\mathrm{ln}\left({x}^{2}-5\right)& =\mathrm{ln}\left(2-x{\right)}^{2}+\mathrm{ln}\left({x}^{2}-5{\right)}^{3}\\ & =\mathrm{ln}\left[\left(2-x{\right)}^{2}\left({x}^{2}-5{\right)}^{3}\right]\end{array}$

Tatiana Cook

Beginner2022-10-10Added 3 answers

$2\mathrm{ln}\left(2-x\right)+3\mathrm{ln}\left({x}^{2}-5\right)=\mathrm{ln}{\left(2-x\right)}^{2}{\left({x}^{2}-5\right)}^{3}$

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?