# Solving for x help

• January 17th 2011, 08:18 PM
agent2421
Solving for x help

3^5+2x = 1/9x

I'm not looking just for the answer (since i have it) but i want to understand it.

Here's my rough work.

3^5+2x = 1/ 9^x

= 3^5+2x = 1 / (3^2)^x

5+2x = 2x

0x = -5

... I know i made a mistake somewhere there... the actual answer is x = -5/4 but I have no idea how you get it since the 2 is not negative...

Thanks.
• January 17th 2011, 08:37 PM
Soroban
Hello, agent2421!

You left out a step . . . and that's where your mistake occured.

Quote:

$3^{5+2x} \:=\: \dfrac{1}{9^x }$

$3^{5+2x} \:=\: \dfrac{1}{9^x}$

$3^{5+2x} \;=\;\dfrac{1}{(3^2)^x}$

$3^{5+2x} \;=\;\dfrac{1}{3^{2x}}$

$3^{5+2x} \:=\: 3^{-2x}$ .
Here!

Got it?

• January 18th 2011, 01:44 AM
Wilmer
Quote:

Originally Posted by agent2421
3^5+2x = 1/9x

Very badly posted; should be: 3^(5 + 2x) = 1 / 9^x