log

_{y}(x) + log

_{x}(y) = 43

What are the values of x and y?

logy(x) + logx(y) = 43

Let,logx(y) = p, so that:

p + 1/p = 43

Or, p^2 - 43p+1 = 0

Or, p = (43 +/- sqrt(1845))/2

= (43 +/-3*sqrt(205))/2

Or, logx(y)

= (43 +/-3*sqrt(205))/2

= 42.9767, 0.0233

So, y = x^42.9767, x^0.0233

Hence, the given equation admits of an infinite

number of solutions corresponding to infinite

choices of x.

*Edited on ***August 21, 2007, 2:56 pm**