Value of x

Algebra Level 2

If x y = y x x^y = y^x and 0 < x < y 0 < x <y , how many possible value(s) of x x are there?

infinity 4 2 1

พันดารา ธุวจิตต์ by พันดารา ธุวจิตต์ , 56, Thailand

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1 solution

The conditions could only be satisfied if y=4 and x=2.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

There are infinite values that satisfy the condition such as 2.7^2.8, 2.6^2.9, 2.5^3, 2.4^3.1, 2.3^3.2, 2.2^3.5, 2.1^3.6,2^4, 1.8^4.8, 1.7^5.7, 1.6^6.6

พันดารา ธุวจิตต์ - 4 years, 10 months ago

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