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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?

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

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