if $5,000 is invested at an interest rate of 5% per year ... › cms › lib02 › sc01001931 ›...
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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
Logarithmic Functions
Section 6.3
Logarithms
Used to find unknown exponents in
exponential models
Define many measurement scales in the
sciences such as the pH, decibel, and Richter
scales.
Logarithmic Function
It’s the inverse of the exponential function
log ya x y a x
Graph: 2( ) logf x x
Domain:
Range:
Graph: 2( ) 3 logf x x
Domain:
Range:
Graph: 2( ) log ( 4)f x x
Domain:
Range:
Graph: 2( ) log ( 2)f x x
Domain:
Range:
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
Write in logarithmic form.
35 125
Write in logarithmic form.
46 1296
Write in logarithmic form.
3 13
27
Natural log
log lne x x
Write in logarithmic form.
2 7.389...e
Write in exponential form.
3log 81 4
Write in exponential form.
8log 512 3
Write in exponential form.
ln(181.3) 5.2
Write in exponential form.
3
1log 2
9
Find the value of x.
4log 64x
Find the value of x.
2log 16x
Find the value of x.
125log 5x
Find the value of x.
5 log 32x
Find the value of x.
34 log x
Find the value of x.
2log 1x
Find the value of x.
1log 9
2x
Find the value of x.
73 log x
Find the value of x.
9log 3x
Find the value of x.
1ln x
e
Solve
( ) ln 44f x x for x
Find to the nearest thousandth – using the calculator.
10( ) log 240f x x for x
Find to the nearest thousandth – using the calculator.
10 85x
Find to the nearest thousandth – using the calculator.
10 22x
Homework
Worksheet