Evaluate (log_{sqrt{2}}4+log_{frac{1}{2}}16-log_{4}32)
-
A.
-5.5 -
B.
-2.5 -
C.
2.5 -
D.
5.5
Correct Answer: Option C
Explanation
Note that if we set (log_{sqrt{2}}4 = x_{1}, hspace{1mm}solvinghspace{1mm}giveshspace{1mm}x_{1}=4\ifhspace{1mm}log_{frac{1}{2}}16 = x_{2}, Rightarrow x_{2} = -4\Also hspace{1mm}forhspace{1mm}log_{4}32 = x_{3} = 2.5\Combininghspace{1mm}results,hspace{1mm}x_{1}+x_{2}+x_{3} = 4+(-4)-2.5=-2.5)
Note that the solution has been separated to simplify solving difficulty due to different bases.