A) 6
B) \[\frac{1}{6}\]
C) \[\frac{6}{5}\]
D) \[\frac{5}{6}\]
Correct Answer: D
Solution :
(d): Let \[\text{lo}{{\text{g}}_{16}}^{64}=n\] Then \[{{16}^{n}}=64\] \[\Rightarrow {{4}^{2n}}=64={{4}^{3}}\] \[2n=3\] \[n=\frac{3}{2}\] Similarly \[\text{lo}{{\text{g}}_{64}}16=\frac{2}{3}\] \[\therefore \text{lo}{{\text{g}}_{16}}64-\text{lo}{{\text{g}}_{64}}16=(n-m)=\left( \frac{3}{2}-\frac{2}{3} \right)=\frac{5}{6}\]
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