perplexus.info :: Just Math : Logarithm Crossed Ordered Pairs Puzzle

Logarithm Crossed Ordered Pairs Puzzle (Posted on 2023-07-30)

Determine the total number of ordered pairs(x,y) of positive integers with 2≤ x,y ≤ 2023 that satisfy this equation:

 x^{log_y(x^-4)} = y^{log_x(yx^-3)}

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

There are precisely 43 ordered pairs that satisfy the given conditions.
For an explanation, refer to the solution submitted by Brian Smith in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Analytic Solution	Brian Smith	2023-07-30 10:13:43
re: computer solution	Charlie	2023-07-30 10:08:52
computer solution	Charlie	2023-07-30 09:43:47
I find ...	Larry	2023-07-30 08:13:50

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