Problem: The logarithm of 27949327 \sqrt[4]{9} \sqrt[3]{9}2749​39​ to the base 333 is
Answer Choices:
A. 8128 \frac{1}{2}821​
B. 4164 \frac{1}{6}461​
C. 555
D. 333
E. none of these Solution:
27⋅94⋅93=33⋅31/2⋅32/3=325/6,3325/6=41627 \cdot \sqrt[4]{9} \cdot \sqrt[3]{9}=3^{3} \cdot 3^{1 / 2} \cdot 3^{2 / 3}=3^{25 / 6}, \quad \log _{3} 3^{25 / 6}=4 \dfrac{1}{6}27⋅49​⋅39​=33⋅31/2⋅32/3=325/6,log3​325/6=461​.