# Prove logarithmic formula is accurate

• Dec 17th 2012, 07:39 AM
lostinlalaland
Prove logarithmic formula is accurate
Hi everyone
I am trying to solve this question
Prove that
LOG4X=LOG2√X

• Dec 17th 2012, 07:48 AM
MarkFL
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:

$\displaystyle \log_a(c)=\frac{\log_b(c)}{\log_b(a)}$
• Dec 17th 2012, 07:57 AM
lostinlalaland
Re: Prove logarithmic formula is accurate
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
• Dec 17th 2012, 08:00 AM
MarkFL
Re: Prove logarithmic formula is accurate
Yes, a more specific way to go would be to write:

$\displaystyle \log_4(a)=\frac{\log_2(a)}{\log_2(4)}=\frac{\log_2 (a)}{\log_2(2^2)}=$...
• Dec 17th 2012, 08:08 AM
lostinlalaland
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
• Dec 17th 2012, 01:48 PM
Deveno
Re: Prove logarithmic formula is accurate
it is a rule of logarithms that:

logn(ab) = b(logn(a)), even when b = 1/2.....
• Dec 17th 2012, 02:10 PM
skeeter
Re: Prove logarithmic formula is accurate
Quote:

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.
• Dec 19th 2012, 12:43 AM
ibdutt
Re: Prove logarithmic formula is accurate
See the image for solution
• Dec 19th 2012, 01:06 AM
BobP
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 $\displaystyle m=n.$