If $a_1, a_2, a_3,...$ is a geometric sequence with a common ratio $r>0$ and $a_1 > 0$, show that the sequence $\log a_1, \log a_2, \log a_3,... $ is an arithmetic sequence, and find the common difference.
So we know that the first sequence is of the following form: $$a_1, a_2, a_3, \dots = a_1, a_1r, a_1r^2, \dots$$
We also know that the second sequence is of the following form:
$$\log a_1, \log a_2, \log a_3,... = \log a_1, \log a_1 + \log r, \log a_1 + 2 \log r, \dots $$
So the common difference is $\log r$.
I think this is the correct answer as $\log r^n = n \log r$. Is my answer correct?