# [SOLVED] putting a exponential growth function to log form

• Apr 7th 2010, 06:33 PM
kelvinly
[SOLVED] putting a exponential growth function to log form
p(t) = 100*(2^2t)

would i have to multiply the 100 and the 2 or just leave it like that? i'm confusing myself with the logarithmic law..

edit: thank you integral!
• Apr 7th 2010, 07:16 PM
integral
$P(t)=100(2^{2t}) \Rightarrow \frac{P(t)}{100}=2^{2t}$
thus:

$log_2\frac{P(t)}{100}=2t \,\,\,\because \,\,\,a^x=b\Rightarrow log_ab=x$

then:

$\frac{1}{2}log_2\frac{P(t)}{100}=t$

$log_2\sqrt{\frac{P(t)}{100}}=t$

$
log_2\frac{\sqrt{P(t)}}{10}=t$
• Apr 7th 2010, 07:17 PM
Sudharaka
Dear integral,

There is a little typo in the first line. It should be, $P(t)=100(2^{2t}) \Rightarrow \frac{P(t)}{100}=2^{2t}$
• Apr 7th 2010, 07:23 PM
integral
I really meant $2^{2t}$, but thank you (Wink)
• Apr 7th 2010, 07:24 PM
kelvinly
Quote:

Originally Posted by integral
I really meant $2^{2t}$, but thank you (Wink)

yes i know haha. no, thank you!
• Apr 8th 2010, 03:23 AM
HallsofIvy
Quote:

Originally Posted by Sudharaka
Dear integral,

There is a little typo in the first line. It should be, $P(t)=100(2^{2t}) \Rightarrow \frac{P(t)}{100}=2^{2}2^{t}$

No. $2^22^t= 2^{2+ t}$, not $2^{2t}= (2^2)^t= 4^t$.