Problem: If log8​3=p and log3​5=q, then, in terms of p and q,log10​5 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,
log10​5=log10​23pq=3pqlog10​2=3pqlog10​510​.
Since log10​510​=log10​10−log10​5=1−log10​5. we have log10​5=3qp(1−log10​5) and therefore, solving for log10​5, we obtain (D).