[SOLVED] putting a exponential growth function to log form

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April 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!
April 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:

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

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

$<br /> log_2\frac{\sqrt{P(t)}}{10}=t$
April 7th 2010, 07:17 PM
Sudharaka

Dear integral,

There is a little typo in the first line. It should be, $P(t)=100(2^{2t}) \Rightarrow \frac{P(t)}{100}=2^{2t}$
April 7th 2010, 07:23 PM
integral

I really meant $2^{2t}$ , but thank you (Wink)
April 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!
April 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 $2^{2t}= (2^2)^t= 4^t$ .

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