Problem: If x=(log8​2)(log2​8), then log3​x equals:
Answer Choices:
A. −3
B. −31​
C. 31​
D. 3
E. 9
Solution:
​log2​8=3 and log8​2=31​∴x=(31​)3∴log3​x=3log3​31​=​3(0−1)=−3​
or
Let y=log2​8(=3)∴2y=8(=23)∴ylog8​2=log8​8=1
∴log8​2=y1​∴x=y1​y=yy1​=y−y
∴log3​x=−ylog3​y=−3(1)=−3