Tough question...

I have tried to come up with a way to solve. I ended up using Google sheets.

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Luke73 · 26-30, M

The exact solution is exp(W(log(25))) which is about 2.96322 as you calculated.

Where exp is the exponential function (e^x), log is the natural logarithm and W is the product log function, the solution to z=w*exp(w)

Lisa82 · 41-45, F

@Luke73 that's awesome. Thank you.

Domking · 61-69, M

Cool
That is called method of successive approximations. First, one takes an example close to the problem like 3^3=27 which is near 25. Then walk in small steps till the number 25 is crossed.

Lisa82 · 41-45, F

@Domking Lol. That's exactly what I did. Now I know what it's actually called . Thank you

cmmdfghrae · 46-50, M

I don’t blame you, I have forgot a lot as I taught at high school for long time

but I hope this would be useful,

Lisa82 · 41-45, F

@cmmdfghrae yes thank you. been a while

JoyfulSilence · 51-55, M

@cmmdfghrae

How does one compute W? Does one need a numeric approximation?

If so, then her method of trial and error seems easier. Unless software has a module for this function W that converges faster!

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