Suppose that x and y are positive numbers such that \(\log_x y - \log_y x = 3\)
Find \((\log_x y)^2 + (\log_y x)^2\)
+128472 Square both sides
[ log x y]^2 - 2 [ log x y ][log y x ] + [ log y x ]^2 = 9
Using the change of base theorem we have that
log x y * log y x =
[log y / log x] * [ log x / log y] = 1
Sowe have that
[ log x y ]^2 - 2 (1) + [ log y x]^2 = 9 add 2 to both sides
[ log x y ]^2 + [ log y x ]^2 = 11
