Post on 17-Jan-2016
10.8 THE NATURAL LOG FUNCTION
e is : irrational #
like , not variable
2.718
NATURAL LOG
Recall common log:log 2 = log10 2
Natural log: denotedloge x ln x
ln e
BASE E
If ln x = 5, then loge x = 5
then ln 7 = xIf e x = 7,
= lne e= 1
ln ek= k(ln e)
= k(1) = k
e ln 7 = e lne 7 = 7
Same laws & properties of logs apply
to natural logsthen (around the world!), so e 5 = x
then loge 7 = x
EXAMPLE 1) SIMPLIFY
21lne
2lne e
2 lne e 2(1) 2
2ln5 ln 4 3
EX 2) WRITE AS A SINGLE LOG
2 3ln 5 ln 4 lne e e e
33 lne e
3
100ln
e
3
25 4lne e
3
100lne e
Write as ln
( )-12 1e x
ln 2x
SOLVE—LEAVE ANSWERS IN TERMS OF “E”
ln 2e x
2e x
1ln 2x Ex 3) Ex 4)
1ln 2e x
2 1xe
( )-1
2e x
2 ln ln 9e ex e
EX 4) SOLVE (WRITE IN TERMS OF LN)
2ln ln 9xe ee
2 9xe
ln 3x
2 ln 9ex 12 ln 9ex
12ln 9ex
ln 3ex
Take natural log of both sides
ln 1e e
129 9
ln 5x
TOO
5e x
3 64xe 1) 2)
ln 4 x
1ln 7 ln 2 ln8
3
TOO—WRITE AS A SINGLE LOG
7 2ln
2e
ln 7
HOMEWORK
#6 Pg. 490 1 – 33 odd