Is it possible to solve for x, where ln(x), ln(2x) and ln(3x) form a legitimate right triangle?
From: Artofmathematics.com
By the given conditions, we have:
(ln x)^2+ ln(2x)^2 = ln(3x)^2
=> 2(ln x)^2 + ln^2(2) + 2ln(2)*ln(x) = (ln 3)^2 +2ln(3)*ln(x) + ln(x)^2
=> ln(x)^2+ ln^2(2) + 2ln(2)*ln(x) = (ln 3)^2 +2ln(3)*ln(x)
=> 2x/3 = +/- ln(9/4)/ln(3)
=> x = 3/2 *exp(+/-ln(9/4)/ln(3))
=> x =~ 0.58368, 3.8549
Puzzle Answer
