# Difficult exponential equation

1. Jul 29, 2009

### zandria

1. I need to solve the following exponential equation for t.

$$\frac{1}{20} =0.5 e^{-0.877t} - 0.05 e ^{-9.123t}$$

2. Jul 29, 2009

### EternityMech

i think you can take the t out and calculate the 0.5e things with eachohter inside parathensis and put the t outside. check my thread Hardest Math Problem EVAR!!! i had the same problem.

3. Jul 29, 2009

### zandria

Unfortunately, due to the properties of exponentials, I don't think I can take the t out. If the exponents of the exponential were sums instead of products, the problem would be much easier and would allow me to factor out an e^t. But I'm not sure how to isolate the t in this specific equation.

4. Jul 29, 2009

### Staff: Mentor

Nothing obvious comes to my mind, so you might need to calculate t by an approximation method. For example, using Excel, the exponential expression on the right side of your equation equals .055819 when t is 2.5. The value you want is slightly larger than 2.5, I believe.

Note to EternityMech: There is no such word in English as "evar."

5. Jul 29, 2009

### EternityMech

w00t?

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