Evaluate log sqrt 2 4 log frac 1 2 16-log 4 32 - JAMB Mathematics 2003 Question
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 option: c
Note that if we set \(log_{\sqrt{2}}4 = x_{1}, \hspace{1mm}solving\hspace{1mm}gives\hspace{1mm}x_{1}=4\if\hspace{1mm}log_{\frac{1}{2}}16 = x_{2}, \Rightarrow x_{2} = -4\Also \hspace{1mm}for\hspace{1mm}log_{4}32 = x_{3} = 2.5\Combining\hspace{1mm}results,\hspace{1mm}x_{1}+x_{2}+x_{3} = 4+(-4)-2.5=-2.5\)
Note that the solution has been separated to simplify solving difficulty due to different bases.
Note that the solution has been separated to simplify solving difficulty due to different bases.
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