How do I solve log_0.25[ (log_2 3)(log_3 4)]log0.25[(log23)(log34)] ?

1 Answer
Oct 14, 2017

The answer is -1/212.

Explanation:

Start by rewrite 0.250.25 as 1/414.

=log_(1/4)[(log_2 3)(log_3 4)]=log14[(log23)(log34)]

We can now use the change of base formula, which states that log_a n =logn/logalogan=lognloga.

=log_(1/4) [ (log3)/(log2) * log4/log3]=log14[log3log2log4log3]

=log_(1/4) (log4/log2)=log14(log4log2)

=log_(1/4) (log(2^2)/log2)=log14(log(22)log2)

=log_(1/4) ((2log2)/log2)=log14(2log2log2)

=log_(1/4) 2=log142

Once again we use the change of base formula.

=log2/(log(1/4)=log2log(14)

=log2/(log2^-2)=log2log22

=log2/(-2log2)=log22log2

=-1/2=12

Hopefully this helps!