# Swing the Logarithmic Curve around (1, 0)

Swing the Logarithmic Curve around (1, 0)

The logarithmic function to the base , where and , is defined by if and only if ; the domain is and the range is .

b

b>0

b≠1

y=x

log

b

x=

y

b

0<x<∞

-∞<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 and . Also notice where the blue curve lies in relation to the common logarithm (base 10) and the natural logarithm .

0<b<1

b>1

log

ln