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
Explanation:
Start by rewrite
=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_(1/4) [ (log3)/(log2) * log4/log3]=log14[log3log2⋅log4log3]
=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)=log2log2−2
=log2/(-2log2)=log2−2log2
=-1/2=−12
Hopefully this helps!