Ask Me Help Desk - Find a power in equations

Hey,

Me again,

Ok so the is a= 15.3 x 0.88608860^t

And I have the value for a which is 7.65, how do I work out what t is? Please give me step by step explanation

thank you in advance..

DD

Quote:

Me again,

Ok so the [something] is a= 15.3 x 0.88608860^t

And I have the value for "a" which is 7.65, how do i work out what "t" is?

Hi "Me".

$a= 15.3 \, \times \, 0.88608860^t$

$7.65 = 15.3 \, \times \, 0.88608860^t$

To find the power, you need to take the logarithm of both sides. It doesn't matter what the base of the logarithm is. It can be the common log (base 10), the natural log (ln = base e), or any other log.

$log(7.65)=log(15.3\, \times \, 0.88608860^t)$

$using\,\, log(a b) = log(a) + log(b)$

$log(7.65)=log(15.3) + log(0.88608860^t)$

$using\,\, log(a^b) = b \, log(a)$

$log(7.65)=log(15.3) + t\, log(0.88608860)$

$\frac {log(7.65)-log(15.3)}{log(0.88608860)}= t \,\approx\,5.73141$

$7.65=(15.3)\cdot .8860886^{t}$

$.5=.8860886^{t}$

$ln(.5)=tln(.8860886)$

$\frac{ln(.5)}{ln(.8860886)}=t\approx 5.732$

You have it correct, P, I just think you typoed at the end.

$\frac{log(7.65)-log(15.3)}{log(.886-886)}\approx 5.732$

Yup, I got 5.73141006...

Me, too. I just have to quit falling asleep with "calculator".