Let , where is an integer and . The difference between the largest and smallest…

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

Problem

Let

\log_a n=\alpha+\beta

, where

\alpha

is an integer and

\beta\in[0,1)

. The difference between the largest and smallest integral values of

n

satisfying

\alpha=3

and

a=5

is (1) 499 (2) 500 (3) 501 (4) 502