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A couple of Logs (Posted on 2002-06-04) Difficulty: 4 of 5
logy(x) + logx(y) = 43

What are the values of x and y?

See The Solution Submitted by Dulanjana    
Rating: 2.4375 (16 votes)

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Solution Solution To The Problem | Comment 15 of 17 |

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
  Posted by K Sengupta on 2007-03-19 11:47:41

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