If and are integers such that

MATHEMATICS · Single correct · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

3\leq a\leq2015

and

3\leq b\leq2015

are integers such that

\log_a b+6\log_b a=5

, then the number of ordered pairs

(a,b)

is (1) 48 (2) 50 (3) 52 (4) 54