True or false:

Question

2 ln x / ln 5 = ln x^2 - ln 5

for all positive values of x.

Answer 1

False.
All we need is one counterexample.
let x = e
LS = 2 ln2/ln5 = 2/ln5
RS = ln e^2 - ln5
= 2lne - ln5
= 2 - ln5
≠ LS

Answer 2

2 lnx/ln 5 = 2ln x - ln 5

only for lnx = ln^2(5)/(2 ln 5 - 2)