What is the sign of expression: abs(cos(x))-log2 (3) ??????

1 Answer
Mar 4, 2018

The expression is smaller than #0# for all #x in RR#, so its sign is #-#.

Explanation:

Firstly, let's assume #|cos x| - log_2 3 <0# , #forall x in RR#.

By adding #log_2 3# onto both sides, we have

#|cos x| < log_2 3#

Raising #2# to both sides :

#2^|cos x| < 3#

The maximum value of #|cos x|# is #1#, therefore the maximum value of #2^|cos x| = 2#.

Since #2^|cos x| < 3# , #forall x in RR#, that means that

#|cos x| - log_2 3 <0#.