Problem: If log83=p and log35=q, then, in terms of p and q,log105 equals
Answer Choices:
A. pq
B. 53p+q
C. p+q1+3pq
D. 1+3pq3pq
E. p2+q2
Solution:
By hypothesis we have 3=8P=23p and 5=3q so 5=(23p)q=23pq. Therefore,
log105=log1023pq=3pqlog102=3pqlog10510.
Since log10510=log1010−log105=1−log105. we have log105=3qp(1−log105) and therefore, solving for log105, we obtain (D).