Find a such that log_(3)(x) = alog_(5)(x) for all values of x > 0 .​

Question

Find a such that

`log_(3)(x) = alog_(5)(x)`
for all values of x > 0 .​

Answer 1

Recall the change-of-base formula:

`\log_5x=(\log_3x)/(\log_35)`

(you can insert any logarithm on the right side)

It follows that
`a=\log_35`.