-12.5exp(-1500t) + 16exp(-2400t) + exp(-600t) = 0

solve for t. I don't know how to take the natural log of a sum of exponentials. thanks for your help!

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- February 26th 2010, 09:29 AMlistonrouteEquation involving sum of exponentials
-12.5exp(-1500t) + 16exp(-2400t) + exp(-600t) = 0

solve for t. I don't know how to take the natural log of a sum of exponentials. thanks for your help! - February 26th 2010, 11:07 AMebaines
There may be an easier way, but here goes:

Starting with

Divide through by , and rearrange:

This factors out to the form:

(eqn 1)

Where and . You have two equations in two unknowns, which gets you to:

Use the quadratic formula to solve for A:

1.448 or 11.052, B = 12.5-A = 11.052 or 1.448

Put these values back into the equation (1):

So:

or:

- February 26th 2010, 11:45 AMlistonroute
awesome

- February 26th 2010, 01:09 PMSoroban
Hello, listonroute!

Another approach . . .

Quote:

Solve for

I don't know how to take the natural log of a sum of exponentials.

Nobody does!

We have: .

Multiply by

Let

Quadratic Formula: .

Back-substitute: .

. . Therefore: .

- February 26th 2010, 01:32 PMlistonroute
very nice as well, thanks. I should've seen this...been out of practice too long I suppose.