How do I solve this equation for x - finding the maximum domains?

[itzela]

I have a problem solving this equation for x - finding the maximum domains.

3(2^(2x+1)+5(2^(-x) )= 31

What I did first was to take the logarithim on both sides of the equation... to solve for x. But that apparently isn't a "logical" way to proceed. Any advice?

 

[matt grime]

taking logs won't help. logs don't work well when you're adding things. why take logs anyway? you just want the set of x for which that expression makes sense for whatever rules you have to satsify. For quesitons like this it is 'avoid square roots of -ve numbers, and don't divide by zero'.

 

[itzela]

Ey Dude , I think u didnt get the function fully,it is
[3(2^(2x+1))]+[5(2^(-x)] = 31

^ means to the power of ...

 

[itzela]

I would appreciate any help i could get from anyone that has any idea at all to solve this equation because i have a upcoming exam tomorrow with the similar question like this and i really need help..please i would appreciate all kinds of help that i could get..i just can solve this equation as i have no idea whether to input it with log or should i input it with a different way...any suggestions also would be gladly welcomed...is there another way i could approach this equation as i have tried it with log and it didn't come out so well..so please..any approach??and for assurance that i am not here just that everyone to help me do my homework without me solving i found out with logs that the answer was x=-1.336 which is i wrong i think..please :P

 

[matt grime]

You asked to find the domain of something. I presumed that to be the LHS of the equation. So are you really asking 'how do I solve this for x?' i.e. nothing to do with domains?

 

[Eighty]

Set t=2^x and express your equation in t. Rearrange it a little and you'll get a polynomial. Solve. Then substitute x back and solve for it.

 

[HallsofIvy]

You can't expect people to guess what you want! You titled this "Domains" and your question was "finding the maximum domains". The you show us an equation. That makes no sense at all. There is no such thing as a "domain" for an equation. A function has a domain. And a function has a domain. I don't know what you mean "the maximum domains".

But then you start asking about solving for x- which has nothing to do with finding a domain. If that really is the problem, dp what Eighty suggested: let t= e^x and first solve for t.

Hint: e^-x= 1/e^x= 1/t and e^2x+1= e^2xe¹= e(e^x)²= et².