How Do You Solve an Exponential Inequality with Different Bases?

[scientifico]

Homework Statement

2^x + 2^(4-x) > 17

2.The attempt at a solution
I factorized for 2^(-x) so I have 2^(-x) * (16 + 2^(2x)) > 17 but I don't know what to do after... could you help me ?

thanks

 

[SammyS]

Homework Statement

2^x + 2^(4-x) > 17

2.The attempt at a solution
I factorized for 2^(-x) so I have 2^(-x) * (16 + 2^(2x)) > 17 but I don't know what to do after... could you help me ?

thanks

Let u = 2^x .

 

[scientifico]

how does it become ?

 

[vela]

That's what you're supposed to figure out and show us.

 

[scientifico]

Thanks I figured it out and solved correctly.

(u^2 - 17u +16)/u > 0

 

[SammyS]

Thanks I figured it out and solved correctly.

(u^2 - 17u +16)/u > 0

What did you get when you solved for x ?