Question

When expanding ln to a fraction, do you only distribute it to the numerator?

Answer 1

\[a\times\frac{b}{c}=\frac{ab}c\]

Answer 2

Okay, great, thank you!

Answer 3

or you "could" go
\[a\times\frac{b}{c}=\frac{b}{c/a}\]

Answer 4

In my problem I have to expand the problem ln(2x^6+3squareroot(x+8)/(x-1)^4

Answer 5

So just distributing to the numerator, assuming ita ln/1 would prbably be best, I think?

Answer 6

where is the closing bracket on the natural log?

Answer 7

It is supposed to be applied to the whole fraction.... sorry if it was confusing!

Answer 8

\[\ln\left(\frac{2x^6+3\sqrt{(x+8)}}{(x-1)^4}\right)\]?

Answer 9

Yes!

Answer 10

well the thing about logs ...

\[\log ab=\log a+\log b\]
\[\log \frac ab=\log a-\log b\]

Answer 11

So would I turn the numerator into ln((2x^6)(3sq.rt.x+8))?

Answer 12

where'd the plus go?

\[\log a+b≠\log a+\log b=\log ab\]

Answer 13

Oh! I missunderstood. So now I have \[\ln \left( 2x ^{6} \right)+ \ln \left( 3\sqrt{x+8} \right)\]

Answer 14

In the numerator.

Answer 15

Thanks for all your help!

Answer 16

no you cant do that the whole numerator will stay in a single log,

however you can simplify the log of the denominator