Solve 9^x - 6^x - 2^(2x+1) = 0 for x

[DrSploc]

Hi, I'm preparing for an admission test to a university and browsing through the earlier tests I found some questions quite hard to solve.
I think I'll use this thread to ask questions concerning the test questions.
Okay so here is one I couldn't even solve with the help of my tutor:

9^x - 6^x - 2^(2x+1) = 0

The question is: how many solutions does the equation have? 0, 1, 2 or other?
Now I don't even know where to start.
All help would be appreciated.

/DrSploc

 

[Deleted member 4993]

Hi, I'm preparing for an admission test to a university and browsing through the earlier tests I found some questions quite hard to solve.
I think I'll use this thread to ask questions concerning the test questions.
Okay so here is one I couldn't even solve with the help of my tutor:

9^x - 6^x - 2^(2x+1) = 0

The question is: how many solutions does the equation have? 0, 1, 2 or other?
Now I don't even know where to start.
All help would be appreciated.

/DrSploc

Use wolframalpha and plot the function!

To do it analytically:

substitute:

u = 3^x and v = 2^x

and tell us what do you get.