Hi everyone
I am trying to solve this question
Prove that
LOG_{4}X=LOG_{2}√X
Thanks in advance
Thanks for the quick reply.
What I understood is that I should treat it as change base of log4x to base 2
Though I am sure you are pointing me in the correct direction my brain is dead after looking at this for the past 2 hours
Why bother with change of base ? You don't need it, (and I always struggle to remember it anyway, I finish up having to look it up to be sure I'm remembering it correctly).
Let $\displaystyle \log_{4}X=m, \text{ then } X=4^{m}............(1)$
Let $\displaystyle \log_{2}\sqrt{X}=n, \text{ then } \sqrt{X}=2^{n} \Rightarrow X=4^{n}............(2)$
Comparison of (1) and (2) shows that $\displaystyle m=n.$