# How to solve this logarithm without using the change of base formula?

I'm doing an assignment on logarithms, and I've stumbled upon a tricky question. The task looks like this:

http://puu.sh/5Gcll.png

For the first 3 I have no problem. However, for d) I have no idea where to begin. I just can't see any way to solve it without using the change of base formula. Can anyone help?

• Do you remember that, whatever could be the base, a log(b) = log(b^a) ? – Claude Leibovici Dec 8 '13 at 17:35

Beyond what is in the comments, that $5\log_5(13)=\log_5(13^5)$, you can't do anything else. It is shown here that $\log_5(13)$ must be irrational.