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

In summary, the conversation revolves around the problem of solving the equation 3(2^(2x+1)+5(2^(-x))= 31 for x and finding the maximum domains. The initial approach of taking logarithms on both sides is deemed illogical, and the suggestion to avoid square roots of negative numbers and not divide by zero is given. However, it is later clarified that the main concern is how to solve for x, and the suggestion to substitute t=2^x and express the equation in terms of t is given. The conversation ends with a reminder to be clear and specific when asking for help.
  • #1
itzela
34
0
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?
 
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  • #2
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'.
 
  • #3
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 ...
 
  • #4
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 tommorrow 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
 
  • #5
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?
 
  • #6
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.
 
  • #7
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= ex and first solve for t.

Hint: e-x= 1/ex= 1/t and e2x+1= e2xe1= e(ex)2= et2.
 

1. What is the purpose of finding the maximum domains?

The purpose of finding the maximum domains is to determine the maximum number of unique website addresses that can be registered or used within a specific domain extension (such as .com or .org).

2. How is the maximum number of domains calculated?

The maximum number of domains is calculated by using a mathematical formula based on the number of characters allowed in a domain name and the number of possible combinations of those characters.

3. Are there any limitations to the maximum domains that can be registered?

Yes, there are limitations to the maximum domains that can be registered. Some domain extensions have a set limit on the number of characters allowed in a domain name, while others may have restrictions on certain words or phrases that can be used.

4. How is finding the maximum domains helpful for businesses or individuals?

Finding the maximum domains can be helpful for businesses or individuals who are looking to create a strong online presence. It allows them to choose a unique and memorable domain name that is still available for registration.

5. Is it possible for the maximum domains to change over time?

Yes, the maximum domains can change over time as new domain extensions are created and as the rules and restrictions for existing extensions may be updated. It is important to regularly check the maximum domains for a specific extension before registering a domain name.

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