# Math Help - Solving Exponential Equations

1. ## Solving Exponential Equations

Hi everyone,

I am stumped on a question that I have been wondering about for the whole day. I know that 2^2+3^2=13.. but I wondered what would happen if the exponents were variables....

2^x+3^x=13

Would there be any possible way to solve this equation?

2. Yes there is, with the help of the logarithm function.

$log A^B= B log A$

so take the log of both sides to get: $log2^x + log3^x = log13$

Now apply the property $log A^B= B log A$ and you would be able to solve for x.

3. Hmm.. it doesn't seem to work, because I get 1.4 something if I use that method.

4. Sorry, my mistake. log only works if you want to solve 2^x = 13.

Other than trial and error, I don't know any other way. Sorry.

5. They're different bases, aren't they? In a problem I had tried to take away $4^x-2^x$ but the person said you can't do it if they're different bases.

Idk though. It's a Pythagorean triple.