The given curves are y = 3x and y = log3x.
Clearly, y = log3x is the image of the curve
y = 3x with respect to the line y = x.
Therefore, 3x .log3 = 1
⇒ 3x = 1/log3 = (log3)–1
⇒ x = log3(log3)–1 = – log3(log3)
when x = –log3(log 3), then y = 1/log3
Thus, the point (–log3(log 3), 1/log3) **** on the curve
y = 3x.
Since the curve y = log3x is the image of the curve y = 3x with respect to the line y = x, so the point on the curve y = log3x is
(1/log3 , –log3(log3))
Hence, the shortest distance
