How would you solve the following exponential equations???

answer is2and3. But i want to know the method to solve it.

I will be much thankful to you.

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- November 22nd 2008, 10:12 PMShyamsolve exponential equations
How would you solve the following exponential equations???

answer is**2**and**3**. But i want to know the method to solve it.

I will be much thankful to you. - November 28th 2008, 03:27 AMfardeen_gen
I am trying to solve this problem right from the morning but I am still unsuccessful.(Worried)

Its very simple(as we have the answers) to say:

x^x + y^y = 31 = 4 + 27 = 2^2 + 3^3

x^y + y^x = 17 = 8 + 9 = 2^3 + 3^2

So comparing both sides of the equations, we see that x = 2 and y = 3

Can the MHF helpers please throw some light on what method is to be adopted to solve this type of problem? - December 2nd 2008, 05:04 AMfardeen_gen
I have scoured the internet ever since, but no successful discoveries...(Worried)

- December 16th 2008, 12:05 PMElliPlease help Shyam
Can somebody please find the answer? (Wait)

- December 16th 2008, 12:38 PMIsomorphism
- January 15th 2009, 05:17 PMFreeTSimultaneous Equation?
Considering we have 2 unknowns, and 2 equations, I would imagine that it could be solved with simultaneous equations (eventually).

Here's what I could do:

Substituting x into we get:

That's as far as I've gotten, I'll think about it more later. If anyone else has any more ideas, please post.

Hope I helped.