If log base 2 of x and log base 2 of y are distinct positive integers and log base x of 2 plus log base y of 2 equal to 0.5. xy=?

Answer 1

log_2(x) = 1/log_x(2), so

If log_2(x) = a and log_2(y) = b, we have

1/a + 1/b = 1/2
1/3 + 1/6 = 1/2

so, x=2^3 and y=2^6 so xy = 512