Question

Write each expression as a single logarithm
2 log(x) + 3 log(x+1)

Answer 1

a log(x) can be written as \(\log(x^a)\)

So, 2 \(\log(x)\) = ?

Answer 2

log(x^2)?

Answer 3

Right. Similarly do with 3 log(x+1)

Answer 4

3 log(x+1) = log(x+1)^3

Answer 5

Very good! So, you get :

\(2 \log x + 3 \log(x+1) = \log (x^2) + \log (x+1)^3 \)

Now, use : log a +log b = log (ab)

Answer 6

log(x^2) * log(x+1)^3

Answer 7

No, it you have to put a and b in single log.

That is : \(\log ( (x^2) \times (x+1)^3 ) \)

Answer 8

can that be simplified?

Answer 9

Well, you can expand (x+1)^3 and then multiply x^2 and it .

Answer 10

But, I think, if you put like the above expression only, it will be fine too!

Answer 11

Thanks, I have one more to post so I will close this question

Answer 12

Sure. Tag me there, I will try to help.

Answer 13

Ok I will do that :)