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If $5,000 is invested at an interest rate of 5% per year, find
the amount of the investment at the end of 5 years for the
following compounding methods:
Annually
Monthly
Quarterly
Continuously
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Logarithmic Functions
Section 6.3
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Logarithms
Used to find unknown exponents in
exponential models
Define many measurement scales in the
sciences such as the pH, decibel, and Richter
scales.
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Logarithmic Function
It’s the inverse of the exponential function
log ya x y a x
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Graph: 2( ) logf x x
Domain:
Range:
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Graph: 2( ) 3 logf x x
Domain:
Range:
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Graph: 2( ) log ( 4)f x x
Domain:
Range:
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Graph: 2( ) log ( 2)f x x
Domain:
Range:
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For any positive base b, where b≠1:
bx = y if and only if x = logby
Exponential Form Logarithmic Form
310 1000 10log 1000 3
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Write in logarithmic form.
35 125
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Write in logarithmic form.
46 1296
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Write in logarithmic form.
3 13
27
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Natural log
log lne x x
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Write in logarithmic form.
2 7.389...e
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Write in exponential form.
3log 81 4
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Write in exponential form.
8log 512 3
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Write in exponential form.
ln(181.3) 5.2
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Write in exponential form.
3
1log 2
9
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Find the value of x.
4log 64x
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Find the value of x.
2log 16x
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Find the value of x.
125log 5x
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Find the value of x.
5 log 32x
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Find the value of x.
34 log x
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Find the value of x.
2log 1x
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Find the value of x.
1log 9
2x
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Find the value of x.
73 log x
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Find the value of x.
9log 3x
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Find the value of x.
1ln x
e
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Solve
( ) ln 44f x x for x
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Find to the nearest thousandth – using the calculator.
10( ) log 240f x x for x
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Find to the nearest thousandth – using the calculator.
10 85x
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Find to the nearest thousandth – using the calculator.
10 22x
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Homework
Worksheet