• question_answer Evaluate: $\text{lo}{{\text{g}}_{16}}64-\text{lo}{{\text{g}}_{64}}16$ A)  6                                B)  $\frac{1}{6}$C)  $\frac{6}{5}$                             D)  $\frac{5}{6}$

(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 $\text{lo}{{\text{g}}_{64}}16=\frac{2}{3}$ $\therefore \text{lo}{{\text{g}}_{16}}64-\text{lo}{{\text{g}}_{64}}16=(n-m)=\left( \frac{3}{2}-\frac{2}{3} \right)=\frac{5}{6}$