Hello

I'm confused as to how to do this question.

4^x + 6(4^-x) = 5

I was thinking of changing 4^x to a variable like 'a' so it would be easier to work with, but 4^-x is not the same so I can't replace that with 'a' as well.

Then I though 4^-x = 1/4 ^x
So
4^x + 6[(1/4)^x] = 5

But i have no idea where I'm going with this and I'm lost.

Please help, thanks

I think you're on the right track.

 

4^x + 6∙4^–x = 5

 

You set 4^x = a

 

Then you thought 4^–x = 1/(4^x)

 

Good! That makes 4^–x = 1/a, and so, you've simplified that term too.

 

So now you have a +6/a = 5

 

You don't like this? Go ahead and solve it. It will start to look familiar as you work through it. You will grin, honest. After you solve for a, then solve for x.

I would guess this is the culmination of an algebra course as it combines several facts about equations and their solution?

 

How would you normally solve an equation with x in the power?

 

There are some other steps to take to put this equation into a suitable form before you can take this action, you will need to change this equation into a quadratic to solve it,

Thanks guys, it is a quadratic. I was close!