Problem: If x=(log82)(log28), then log3x equals:
Answer Choices:
A. −3
B. −31
C. 31
D. 3
E. 9
Solution:
log28=3 and log82=31∴x=(31)3∴log3x=3log331=3(0−1)=−3
or
Let y=log28(=3)∴2y=8(=23)∴ylog82=log88=1
∴log82=y1∴x=y1y=yy1=y−y
∴log3x=−ylog3y=−3(1)=−3