Can someone explain step by step how to make x the subject in an exponential equation

Delos · #1 May 17, 2009, 09:04 AM

Can someone explain step by step how to make x the subject in an exponential equation?

I know the general form is y = ae^kx
So the just say I need to find out at what time would the experiment be at its half life which is 50, so I sub 50 into the following equation:

y = 92.776e^(-0.701t)
50=92.776e^(-0.701t)

I'm really bad at exponentials, could someone help? Step by step would be much appreciated

also another question,

lnY= mX + ln k

What is the step by step method to make Y the subject??

Thank you in advance...

DD

Unknown008 · May 17, 2009, 09:15 AM

Ok, here it goes:

$y=ae^{kx}$

Put log on both sides:

$ln(y)=ln(ae^{kx})$

$ln(y)=kxln(ae)$

$\frac{ln(y)}{kln(ae)}=x$

$\frac{ln(y)}{k(ln(a) + ln(e))}=x$

$\frac{ln(y)}{k(ln(a) +1)}=x$

However, I don't quite know what you want concerning the half life.

For the second one,

$lnY= mX + ln k$

$Y= e^{(mX + ln k)}$

It's the reverse of the previous process; here's the rule:

$a=b^c$

$log_b a = c$

Perito · May 17, 2009, 09:51 AM

[quote]Can someone explain step by step how to make x the subject in an exponential equation?
/QUOTE]

Just remember that $Log(A^B) = B\, Log(A)$

That removes the exponent from the equation and makes it solvable by normal algebra. If it's in the form

$A^B=something$

you need to take the logarithm of both sides, first.



At Ask Me Help Desk you can ask questions in any topic and have them answered for free by our experts. To ask questions or participate in answering them you must register for a free account. By registering you will be able to: Get free answers from experts in any of our 300+ topics. Accept money for answers that you provide. Communicate privately with other members (PM). See fewer ads. Sign Up!