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## Homework Statement

Problem: find t in the following equation

## Homework Equations

[tex]64000e^{-1600t}+4000e^{-400t}=50000e^{-1000t}[/tex]

## The Attempt at a Solution

I know the answer: [tex]t=6.17\cdot\;10^{-4}s[/tex]. But I'm struggling with how to get there. This is my attempt:

Factorizing down to:

[tex]1000(64e^{-1600t}+4e^{-400t}-50e^{-1000t})=0[/tex]

and further on:

[tex]1000e^{-400t}(64e^{-1200t}+4-50e^{-600t})=0[/tex]

I realize only what's in the paranthesis is needed, since the 1000e...is never zero:

[tex](64e^{-1200t}+4-50e^{-600t})=0[/tex]

I want to ln both sides, but I'm not quite sure how to do that, since there are three parts...