Answer
Arithmetic sequence with common difference $\log r$
Work Step by Step
We are given the geometric sequence:
$$a_1,a_2,a_3,\dots,...$$
where $a_{k+1}=a_kr,r>0$.
Consider the sequence:
$$\log a_1,\log a_2,\log a_3,\dots$$
We calculate the difference of two consecutive terms:
$$\log a_{k+1}-\log a_k=\log \dfrac{a_{k+1}}{a_k}=\log\dfrac{a_kr}{a_k}=\log r$$
So the second sequence is arithmetic, its common difference being $\log r$.
