Question

@zepdrix

Answer 1

@zepdrix

Answer 2

@zepdrix @iGreen @mathmale @mathmath333 @mathstudent55 @dan815 @Michele_Laino

Answer 3

lol wow that's a lot of @zepdrix

Answer 4

lol

Answer 5

\[\large\rm \ln\left[\sqrt{\frac{x-1}{x^3}}\right]=\ln\left[\left(\frac{x-1}{x^3}\right)^{1/2}\right]\]

Answer 6

Ok with the square root being turned into half power?
Next, apply this rule: \(\rm log(a^b)=b\cdot log(a)\)

Answer 7

ummm....how does that relate to ln?

Answer 8

what? ln=log

Answer 9

I thought ln = log_e (x)

Answer 10

which is a log, yes? :D
so it follows the log rules.

doesn't matter if it's pine, redwood, oak, cedar,
it's a log.

Answer 11

\(\large \color{black}{\begin{align}
& \ln \sqrt{\dfrac{x-1}{x^{3}}}\hspace{.33em}\\~\\
& =\dfrac{1}{2}\times \ln \left(\dfrac{x-1}{x^{3}}\right)\hspace{.33em}\\~\\
& =\dfrac{1}{2}\left( \ln (x-1)-\ln x^{3}\right)\hspace{.33em}\\~\\
& =\dfrac{1}{2}\left( \ln (x-1)-3\ln x\right)\hspace{.33em}\\~\\
\end{align}}\)

Answer 12

Oh, I was just confused cause you didn't put any base. So like this:
\(\Large \frac{1}{2}\log_e{\frac{x-1}{x^3}}\)

Answer 13

Oh I made it look like base 10 >.< ya my bad.
Sure you could do that.

Answer 14

okay, then do I apply the quotient rule of logs?

Answer 15

Yes, seems good.
As mathmath detailed.

Answer 16

Just make sure that you realize the 1/2 is multiplying BOTH logs after you apply that rule.

Answer 17

Oh, okay thank you. I see mathmath kept it in ln form...That's still a logarithmic function, right? so it would be an okay form for this question?

Answer 18

cause the question says write as sum, difference, etc. of logarithms

Answer 19

Yes, leave it as ln :)
I guess I could have posted the log rule like this: \(\rm ln(a^b)=b\cdot ln(a)\)

Answer 20

ok, thank you