Swing the Logarithmic Curve around (1, 0)

base

2

The logarithmic function to the base

b

, where

b>0

and

b≠1

, is defined by

y=

log

b

x

if and only if

x=

y

b

; the domain is

0<x<∞

and the range is

-∞<y<∞

.

Move the slider; the base of the logarithm changes and you see its graph swing around the point

(1,0)

.

Closely observe the two cases

0<b<1

and

b>1

. Also notice where the blue curve lies in relation to the common logarithm

log

(base 10) and the natural logarithm

ln

.