Prove logarithmic formula is accurate

Printable View

December 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

Thanks in advance
December 17th 2012, 07:48 AM
MarkFL

Re: Prove logarithmic formula is accurate

Hint: prove the identity:

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

with the change of base formula:

$\log_a(c)=\frac{\log_b(c)}{\log_b(a)}$
December 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
December 17th 2012, 08:00 AM
MarkFL

Re: Prove logarithmic formula is accurate

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

$\log_4(a)=\frac{\log_2(a)}{\log_2(4)}=\frac{\log_2 (a)}{\log_2(2^2)}=$ ...
December 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
December 17th 2012, 01:48 PM
Deveno

Re: Prove logarithmic formula is accurate

it is a rule of logarithms that:

log_n(a^b) = b(log_n(a)), even when b = 1/2.....
December 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.
December 19th 2012, 12:43 AM
ibdutt

1 Attachment(s)

Re: Prove logarithmic formula is accurate

See the image for solution
December 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 $\log_{4}X=m, \text{ then } X=4^{m}............(1)$

Let $\log_{2}\sqrt{X}=n, \text{ then } \sqrt{X}=2^{n} \Rightarrow X=4^{n}............(2)$

Comparison of (1) and (2) shows that $m=n.$

All times are GMT -8. The time now is 01:26 AM.