Math help with notable limit

[Spart]

I have an issue solving this limit:

 

[latex]\lim_{x\to 0}\frac{\; ln\left (1+3x \right )\; }{x}[/latex]

 

The answer is 3, however I'm not sure how it's obtained. I know that [latex]\lim_{x\to 0}\frac{\; ln\left (1+x \right )\; }{x} = 1[/latex] but I can't quite figure out how to implement this property on the problem above. Could someone please give me a step-by-step explanation on how it should be solved? That would be great!

 

 

[Cap'n Refsmmat]

It seems like L'Hopital's Rule would suffice to solve this problem. Have you tried that?

[Spart]

It seems like L'Hopital's Rule would suffice to solve this problem. Have you tried that?

 

I haven't heard of it as far as I know. Am I obliged to use it or is there another way?

[Nehushtan]

If you have proved that [latex]\lim_{x\to0}\frac{\ln(1+x)}x=1[/latex] (which can be done by L’Hôpital’s rule) then you can use it to deduce the given limit.

 

Hint: Let [latex]y=3x[/latex] and write the denominator in terms of [latex]y[/latex].

Edited March 25, 2013 by Nehushtan