fx=loga x =log xlog af'x=1x log aSince 0 0, f'x=1x log a 0

Type F Ques 1

Type F Ques 1 T eF Lo lthmic Functions Show that f(x) loga x, is a decreasing function for all x>0.

f (x) = \log_{a} x = \frac{\log x}{\log a} f' (x) = \frac{1}{x \log a} Since 0 < a < 1 and x > 0, f' (x) = \frac{1}{x \log a} < 0 . So, f (x) is decreasing for all x > 0 .