# Trying to isolate a variable, but it's hanging out in two exponents

• Sep 10th 2012, 10:09 AM
edthatalkinhorse
Trying to isolate a variable, but it's hanging out in two exponents
Hi everyone. I'm hoping this is the right board to post to, if not please direct me to where I need to be.

Long story short, I had a long crazy equation, and I needed to isolate the variable t so I can shove it into a second equation. I did a lot of work on it, but I've hit a wall now. What is the next step?? Here's the side of the equation I'm doing the work on:

t(1 + 2exp(6-t) + exp(16-(6t/5) )

Any help or suggestions would be very greatly appreciated!
• Sep 10th 2012, 04:12 PM
topsquark
Re: Trying to isolate a variable, but it's hanging out in two exponents
Quote:

Originally Posted by edthatalkinhorse
Hi everyone. I'm hoping this is the right board to post to, if not please direct me to where I need to be.

Long story short, I had a long crazy equation, and I needed to isolate the variable t so I can shove it into a second equation. I did a lot of work on it, but I've hit a wall now. What is the next step?? Here's the side of the equation I'm doing the work on:

t(1 + 2exp(6-t) + exp(16-(6t/5) )

Any help or suggestions would be very greatly appreciated!

I would say it's impossible without using an approximation You might be able to use the Lambert W function here.

But I can't say for sure. You gave us an expression, not an equation. Could you show us the whole problem?

-Dan
• Sep 10th 2012, 04:24 PM
MaxJasper
Re: Trying to isolate a variable, but it's hanging out in two exponents
Can you give us both original equations?
• Sep 10th 2012, 05:56 PM
HallsofIvy
Re: Trying to isolate a variable, but it's hanging out in two exponents
Quote:

Originally Posted by edthatalkinhorse
Hi everyone. I'm hoping this is the right board to post to, if not please direct me to where I need to be.

Long story short, I had a long crazy equation, and I needed to isolate the variable t so I can shove it into a second equation. I did a lot of work on it, but I've hit a wall now. What is the next step?? Here's the side of the equation I'm doing the work on:

t(1 + 2exp(6-t) + exp(16-(6t/5) )

Your first problem is that this is NOT an equation- there is no way to "solve" just an expression.

Quote:

Any help or suggestions would be very greatly appreciated!
Since you choose NOT to tell us what the original problem is, or give us anything helpful, there simply is no way to respond.
• Sep 10th 2012, 06:15 PM
edthatalkinhorse
Re: Trying to isolate a variable, but it's hanging out in two exponents
Ah sorry I guess I got tunnel vision working on it. The original equation was:

S = ([1/(1+exp(10-t/5)) + 1 - 1/(1+exp(6-t))]Lt ) / (V+1-(1/V))

Which I worked around to get to:

t(1 + 2exp(6-t) + exp(16-(6t/5) ) = (S(V+1-(1/V))) / L
• Sep 10th 2012, 06:42 PM
topsquark
Re: Trying to isolate a variable, but it's hanging out in two exponents
Quote:

Originally Posted by edthatalkinhorse
Ah sorry I guess I got tunnel vision working on it. The original equation was:

S = ([1/(1+exp(10-t/5)) + 1 - 1/(1+exp(6-t))]Lt ) / (V+1-(1/V))

Which I worked around to get to:

t(1 + 2exp(6-t) + exp(16-(6t/5) ) = (S(V+1-(1/V))) / L

I think you are missing a negative sign in there, but no matter...the expression can't be solved for t without approximating.

-Dan
• Sep 10th 2012, 06:44 PM
edthatalkinhorse
Re: Trying to isolate a variable, but it's hanging out in two exponents
Quote:

Originally Posted by topsquark
I think you are missing a negative sign in there, but no matter...the expression can't be solved for t without approximating.

-Dan

Ah dang. I guess it's back to the drawing board for me! Thanks anyway.