Question

Find the limit of log2 x/(log3 (x+3)) as x approaches to infinity.

Answer 1

lhospitals rule?

Answer 2

How to do it?

Answer 3

so is it in indeterminate form?

Answer 4

Are the numbers next to the logs the bases?

Answer 5

Yes.

Answer 6

I guess it would help if we did a change of base on both logs.\[\Large \log_2x=\frac{\ln x}{\ln 2}\]

Answer 7

\[\Large \log_3(x+3)=\frac{\ln(x+3)}{\ln3}\]

Answer 8

Remember your change of base formula? :O

Answer 9

So I guess change of base gives us something like this.\[\Large \frac{\log_2x}{\log_3(x+3)}\quad=\qquad \frac{(\ln3)\ln x}{(\ln 2)\ln(x+3)}\]

Answer 10

Thanks.

Answer 11

\[\Large \frac{\ln3}{\ln2}\cdot\frac{\ln x}{\ln(x+3)}\]Understand how to finish it from there? :3