Solve 2^(2x)=8x for x: Detailed Solution

[abia ubong]

2^(2x)=8x,find the value of x with a detailed solution

 

[HallsofIvy]

You posted a number of questions here- you should know by now that we will NOT "solve for you". What do you KNOW about this problem, what have you tried?

Also, what kind of answer do you expect for this? Are you looking for a formula or would a numerical solution do?

 

[abia ubong]

a number that fits the eqn and how it can be resolved

 

[arildno]

HallsofIvy:
I'm quite certain that the reason why abia ubong posts these "problems" is that he has some need to "embarrass" professionals by giving them tasks they can't solve.

That is, he is just a crackpot of a new kind.

 

[DaveC426913]

This one seems pretty solvable. x=2 is one solution.

 

[saltydog]

Well, uh . . . I don't know what to think about that. I'm interested in the problem though and have attached a plot of it and am curious about what could be said about the general case:

a^{bx}=cx

For example, are there always 2 solutions, 1 or none sometimes?

 

[Data]

If c \neq 0, then this is equivalent to asking whether

e^{\alpha x - \gamma} = x

always has solutions for x. It certainly does not always have a real solution, for example

e^{x}=x

has no real solutions. Such equations do always have complex solutions, though.

 

[theCandyman]

Odd, I just read abia ubong post about himself as a "goat". I saw two as an answer, but I was not sure how to find a general solution.

 

[saltydog]

You know Abia, I think a good idea is to use what Data said and consider under what conditions will the graph:

y(x)=e^{\alpha x-\gamma}

cross the line y=x, you know, when that expression "equals" x. Where they touch is where the solutions are if any. It's getting off the subject I know but it helps to do things like this for practice for future problems right? You know how he got that expression and what alpha and gamma are? Know how alpha and gamma are related to a,b, and c? However, you may not want to do "investigative" work like this. I like to.

 

[JamesU]

this is pretty off topic...But how do you type those equations on this forum?

 

[saltydog]

this is pretty off topic...But how do you type those equations on this forum?

Go to the General Physics forum and scroll down 3 or 4 to the "Introducing LaTex typesetting". Also, you can double click on any equation and a small pop-up window will appear showing you what LaTex commands generated the equation.

 

[abia ubong]

hey arildno y are u taking it so hard on me ,i am 16 and i am a nigerian ,i bet u those and problems like this revolve round school ,so i decided 2 send it 2 the forum and u
say i am testing ur ability , i am disappointed in u especially in u arildno

 

[arildno]

These are NOT the type of questions you'll meet in school.
Most equations are UNSOLVABLE by existing techniques, we can only find arbitrarily good APPROXIMATIONS to many of these.

Since you have posted a number of such equations before, and been told that it is basically impossible to find "the general solution" to them, why do you choose to continue posting them?

 

[abia ubong]

cos they aint related 2 me