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

• abia ubong
In summary, abia ubong is a crackpot who posts unsolvable equations for the amusement of those who are able to solve them.
abia ubong
2^(2x)=8x,find the value of x with a detailed solution

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?

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

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

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

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

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?

Attachments

• eq1.JPG
4.4 KB · Views: 422
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.

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.

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.

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

yomamma said:
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.

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

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?

cos they aint related 2 me

1. How do you solve 2^(2x)=8x for x?

To solve this equation, we will take the logarithm of both sides. The base of the logarithm can be any number, as long as it is consistent on both sides of the equation. Let's use the natural logarithm, ln, for this example.

2. Why do we take the logarithm of both sides?

Taking the logarithm allows us to bring down the exponent, making it easier to solve for x. In this case, it will cancel out the exponent on the left side, leaving us with a simpler equation to solve.

3. What do we do after taking the logarithm?

After taking the logarithm, we will use the logarithm rules to simplify the equation. Then, we will isolate the x variable on one side of the equation and solve for it using algebraic methods.

4. Can we use any base for the logarithm?

Yes, we can use any base for the logarithm as long as it is consistent on both sides of the equation. However, using the natural logarithm, ln, is often the most convenient for this type of equation.

5. Are there any restrictions for the solution of this equation?

Yes, there are restrictions for the solution of this equation. Since we cannot take the logarithm of a negative number, the value inside the parentheses of the logarithm must be positive. This means that the solution for x must be greater than 0.

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