Solve 3^(2x) - 2*3^(x+5) + 3^10 = 0 - Brain Boosting Hint

[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

 

[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.

 

[CFDFEAGURU]

Welcome to the forum.

Please use the homework outline for your posting of homework.

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

Please be specific and show your attempt at a solution and then we can help you out.

Thanks
Matt

 

[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!)

 

[Mark44]

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

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

 

[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.