Page 69 - Math SL HB Sem 1

FUNCTIONS, I,tQtJAt'toN S, INI,.Qt I;\LI'l'll)S

II.'I'TIE I,o(;ARI'I'IIJVIIC FT]NCT.ION

The base a logarithm function y=log,x,x>
0 is the inverse ofthe base a exponential
function y - a',(a> 0,a * l).
The base e logarithm function y
=log.x or / = lnr,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 idenrity
lunction.

lnverse Properties for a. and log, .x

I Baseo : afq"' = x, log,a' :_r o)0, o #1, x>0

2 Basee: efo'=x,lne, =x x>o

Graphs lvith a>t
v
v

Y=log,x

-r

=
The graph of y l6t, x is the rellection the line 7 =:r ofthe graph of y a,
=
(JraJrhs rvith 0<a<l
v

_r

y=log,x

/ = -r of the graph of y=a
The graph of y= 169" -ris the reflection inthc line ,.

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