solve with complete solution and no guessing x^x=39?

X^X=39

Take logs of both sides,

lnX^X=ln39

Using log laws logX^X=XlogX, hence

XlnX=log39

XlnX=1.59

f(x)=X*lnX-1.59

differentiate for x

X=3.17289

If you cant understand how i got that last bit, just draw two graphs on the same axis Y=X^X and Y=39, find where they meet, and that's your answer

There isn't a whole number solution (obvious through trial and error). Think you'd maybe need to use logs to work it out, been a while though! Starting point could be take the natural log of each side.

ln(x^x) = ln(39)

(x)(ln(x)) = ln(39) (I'm pretty sure!)

Don't know from there, differentiate maybe, but that would just give you 0 on the right since ln(39) is a constant. Sorry, out of ideas!

Use logarithms so you can differentiate, then apply Newton's method to f(x)=x*ln(x) to find x for which the function value is ln(39)