# Unsure how to solve exponential equation

• Aug 25th 2009, 09:39 AM
RobLikesBrunch
Unsure how to solve exponential equation
Hi,

I'm helping my brother on his homework, and stumbled across

$4x^2=1.05^x$

I tried using logs to get the x's to one side but always, invariably, end up with something containing $x^\frac {1}{x}$ and do not know how to solve from there.

Any tips on how to solve this? I haven't used logarithms in ages, so perhaps I'm forgetting a certain rule?
• Aug 25th 2009, 12:28 PM
running-gag
Hi

You cannot find any computable form of the solutions
You can find them using graphs
It seems there are 2 solutions around -0.49401 and 0.50621
• Aug 25th 2009, 08:12 PM
RobLikesBrunch
Ah, thanks for the help. According to Mathematica, there's another at 255.667...
• Aug 25th 2009, 09:07 PM
Wilmer
Quote:

Originally Posted by RobLikesBrunch
Ah, thanks for the help. According to Mathematica, there's another at 255.667...

Ya; 255.667270736......
To be solved, such equations require "iteration" ; "hit and miss".