section 4.1 logarithms and their properties. suppose you have $100 in an account paying 5%...
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Section 4.1Logarithms and their Properties
• Suppose you have $100 in an account paying 5% compounded annually.– Create an equation for the balance B after t years– When will the account be worth $200?
• In the previous example we needed to solve for the input
• Since exponential functions are 1-1, they have an inverse
• The inverse of an exponential function is called the common logarithm function or the log function
• In other words
xxy y 10thenlogIf
Example• Simplify the following expressions using logs
16227766.310
00001.010
000,10105
4
• Logarithms are just exponents
• Evaluate the following:
)10log(
)10log(
)000,100log(
10log
1log
• Logarithms are inverses of exponential functions so
• Evaluate
N
N
N
N
N
N
log10
,0forand
)10log(
,anyfor
)1log(222.2log5.7 2
1010)10log( x
Properties of the common Logarithm
btb
bab
a
baab
xx
xx
xxy
t
x
x
y
log)log(
logloglog
loglog)log(
0for10
allfor)10log(
110logand01log
10thenlogIf
log
The Natural Logarithm
btb
bab
a
baab
xxe
xxe
e
xexy
t
x
x
y
ln)ln(
lnlnln
lnln)ln(
0for
allfor)ln(
1lnand01ln
thenlnIf
ln
Evaluate
10
2
1ln
10
100log
)87.0(2210
10010
e
eq
x
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