Question

if log1/2 X <3 and log4 X<2, then
(a) 1/8 13 years ago

Answer 1

see.. in this question a little thing to take care of is base..
you increase the power of a number and u get a larger no...
but that is not the case with numbers between 0 & 1..
so if u increase the power of 1/2 & u will be getting lesser no. than previous..

so we go like this..
suppose log1/2X=3 from here u can calculate X=(1/2)^3=1/8
now what you want is log1/2X should be lesser than 3 hence what..? X should be greater than 1/8..
that is the point..

now from 2nd expression
you need log4X<2 hence what u need is X<16..

now the final solution should be intersection of both..hence the 1st option is correct..

remember the following graph & u will never confuse ever..