Problem: If y=(log2​3)(log3​4)⋯(logn​[n+1])⋯(log31​32) then
Answer Choices:
A. 4<y<5
B. y=5
C. y=6
D. 6<y<7
E. none of these answers
Solution:
Let y be the desired product. By definition of logarithm 2log2​3=3. Raising both sides of this equation to the log3​4 power yields 2(log2​3)(log3​4)=4. Continuing in this fashion, one obtains 2y=32. thus y=5.