# Thread: Prove logarithmic formula is accurate

1. ## Prove logarithmic formula is accurate

Hi everyone
I am trying to solve this question
Prove that
LOG4X=LOG2√X

2. ## Re: Prove logarithmic formula is accurate

Hint: prove the identity:

$\displaystyle \log_{a^n}(b)=\frac{\log_a(b)}{n}$

with the change of base formula:

$\displaystyle \log_a(c)=\frac{\log_b(c)}{\log_b(a)}$

3. ## Re: Prove logarithmic formula is accurate

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

4. ## Re: Prove logarithmic formula is accurate

Yes, a more specific way to go would be to write:

$\displaystyle \log_4(a)=\frac{\log_2(a)}{\log_2(4)}=\frac{\log_2 (a)}{\log_2(2^2)}=$...

5. ## Re: Prove logarithmic formula is accurate

Thanks, nice car by the way
What confuses me is the square root if I follow through the equation I feel I will still end up with an incorrect fraction

6. ## Re: Prove logarithmic formula is accurate

it is a rule of logarithms that:

logn(ab) = b(logn(a)), even when b = 1/2.....

7. ## Re: Prove logarithmic formula is accurate

Originally Posted by lostinlalaland
Hi everyone
I am trying to solve this question
Prove that
LOG4X=LOG2√X
post basic log problems in the pre-university algebra forum ... this is not an advanced algebra problem.

8. ## Re: Prove logarithmic formula is accurate

See the image for solution

9. ## Re: Prove logarithmic formula is accurate

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 $\displaystyle m=n.$