Which of the following is/are true?

Options

A. `log_(2)6ltlog_((1)/(2))"(1)/(5)`
B. `log_(2)5gtlog_((1)/(2))7`
C. `log_(10)12gtlog_(15)13`
D. `log_((1)/(2))3gtlog_((1)/(2))5`

Answer

B, C, D

Explanation

(a) `log_(2)6,log_(2^(-1))"1/5-log_(2)'(1)/(5)log_(2)5`
so `log_(2)6 gt log_(2)5`
(b) `log_(2)5 = + , log_((1)/(2))7 = -` so correct
(c) `log_(10)12 gt 1 , log_(15)13 lt 1` so correct
(d) `log_((1)/(2))3 gt log_((1)/(2))5` (correct) as decreasing