SOLUTION: how do you solve an equation with x as an exponent.... for ex. 7^x=3^x+1

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Question 135115: how do you solve an equation with x as an exponent.... for ex. 7^x=3^x+1
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I hope that you mean 7%5Ex=3%5E%28x%2B1%29 rather than 7%5Ex=3%5Ex%2B1. These are very different animals, and the second one can only be solved by numerical analysis methods.

Given that you meant 7%5Ex=3%5E%28x%2B1%29,

Take the log of both sides:

log%287%5Ex%29=log%283%5E%28x%2B1%29%29

Use log%28x%5En%29=n%2Alog%28x%29 to write:

x%28log%287%29%29=%28x%2B1%29%28log%283%29%29

x%28log%287%29%29=x%28log%283%29%29%2Blog%283%29

x%28log%287%29%29-x%28log%283%29%29=log%283%29

x%28log%287%29-log%283%29%29=log%283%29

x%28log%287%2F3%29%29=log%283%29

x=log%283%29%2Flog%287%2F3%29