SOLUTION: Please help!! I have tried this problem to no end. It is a tqake home homework, not out of a text book. Thanks, Laura solve the given equation: (e^3)x^*e^x^2=e^10

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help!! I have tried this problem to no end. It is a tqake home homework, not out of a text book. Thanks, Laura solve the given equation: (e^3)x^*e^x^2=e^10      Log On


   

Question 78794: Please help!! I have tried this problem to no end. It is a tqake home homework, not out of a text book. Thanks, Laura
solve the given equation: (e^3)x^*e^x^2=e^10
Answer by mathdoc314(58) About Me  (Show Source):
You can put this solution on YOUR website!
+%28e%5E3%29+%2A+x%5Ee+%2A+e%5Ex%5E2+=+e%5E10+
This will turn out pretty easy or else impossible if you take the natural logarithm of both sides and then do something about the x^e and then solve with algebra.
The logarithm rules are:
1. +log%28a%2Ab%29+=+log%28a%29+%2B+log%28b%29+
2. +log%28e%5Ec%29+=+c+
3. +log%28a%5Eb%29+=+log%28a%29+%2A+b
Use rule 1 first:
+log%28e%5E3%29+%2B+log%28x%5E3%29+%2B+log%28e%5Ex%5E2%29+=+log%28e%5E10%29+
Use rule 2 and 3:
+3+%2B+3+log%28x%29+%2B+x%5E2+=+10+
+x%5E2+-+7+%2B+3+log%28x%29+=+0+
I don't think there is a way to solve this algebraically. A person can find numbers for x that work very closely, using graphical or numerical methods and tools. I am sorry that I do not have a name for this type of equation.