Two curves and both pass through and are defined respectively by and

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Two curves

L_1

and

L_2

both pass through

(1,0)

and are defined respectively by

y=\log_{b_1} x

and

y=\log_{b_2} x

, where

b_1,b_2>1

. If

L_1

gives the value

0.6

x=3

while

L_2

gives the value

0.4

x=3

, which curve corresponds to the larger base? State your answer with brief reason.