Page 69 - Math SL HB Sem 1

I.-UNCl'tONs; , ri()uA'l toNS INEQtTALtl'IES
,

8.'TTIE LOGARI'I'II]VIIC FUNC.TION

The base a logarithm function y
= rog.x,-r > 0 is the inverse of the base a exponenriar
lunction y . a' ,la > 0,a + l) .
The base e logarithm function
.y=log" x or y-ln_r,x>0 is the inverse of the base
=
e exponential function y s, .
Because a'and log" -r are inverses composing them in either order gives the identity
function.

lnverse Properties for a, and log" ,r

l. Base o.. ato".' =x,log,a,=x o>0,o11 .x>0

2. Basee.. e'n'=x,lne, =x x>0

( J raphs n,ith a>l
v

y..= x

y=log"x

-Y

1'he graph of y ;69, -r is thc rellection the line y=xof thegraph of y=0,
=
(Jraphs rvith 0<acl
v

Z:'

r

y=log,x

The graph of y = log, -r is the reflection in the line ,
!
.y =.r of the graph of = u .

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