# Exponential equation

1. Jan 11, 2010

### doneitall

Can someone give me a starter hint for this problem? Brain's not working at full speed...

3^(2x) - 2*3^(x+5) + 3^10 = 0

Thanks

2. Jan 11, 2010

### espen180

Here are some rules for exponentials:

$$(a^b)^c=a^{b\cdot c}$$

$$a^b\cdot a^c=a^{b+c}$$

See if you can apply these rules to solve your equation.

3. Jan 11, 2010

### CFDFEAGURU

Welcome to the forum.

Are you just trying to solve for x ... or it's derivative or ... what?

Thanks
Matt

4. Jan 11, 2010

### doneitall

Looking to solve for x. It is a homework problem... one that I assigned. I teach this for a living and although I'm sure there's something relatively simple that I'm missing, for the life of me I don't see it now. This is a review problem in precalculus so it doesn't involve calculus to solve.

I've looked at it as: (3^2)^x - 2 (3^x)(3^5) + 3^10 = 0 but not sure where to go next. I don't want a solution - just a shove in the right direction. (Before I go mad!)

5. Jan 11, 2010

### Staff: Mentor

Rewrite your equation as 32x - 2*35*3x + 310 = 0.

This is an equation that is quadratic in form, so you can use the Quadratic Formula to solve for 3x. After that, you can use logs to solve for x.

6. Jan 11, 2010

### doneitall

Sheesh! I had tried this by letting u = 3^x but made an error and gave up when it didn't work out. Thanks. I feel better now.