A28­6Notes.notebook
October 27, 2015
Algebra 2
Ch.8 Notes Page 51
P51 8­6 Natural Logarithms
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The Natural Logarithmic Function
If y = ex , then loge y = x , which is usually written ln y = x
The natural log function is the inverse, y = ln x
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A28­6Notes.notebook
October 27, 2015
Simplifying Natural Logarithms
The properties of common logs also apply to natural logs.
Write as a Single Natural Logarithm
3 ln 6 ­ ln 8
3 ln x + ln y
1/4 ln 3 + 1/4 ln x
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Solving Natural Log Equations
Remember the base of a Natural Log is e.
ln (3x + 5)2 = 4
ln x = .1
ln (x+2) = 12
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A28­6Notes.notebook
October 27, 2015
Solving Exponential Equations
ex+1 = 30
7e2x + 2.5 = 20
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Investment Example
An investment of $100 is now valued at $149.18.
The interest rate is 8%, compounded continuously.
About how long has the money been invested?
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A28­6Notes.notebook
October 27, 2015
Space Example
A spacecraft can attain a stable orbit 300 km above Earth if it reaches a velocity of 7.7 km/s. The formula for a rocket's maximum velocity v in kilometers per second is v = ­.0098t + c ln R. The booster rocket fires for t seconds and the velocity of the exhaust is c km/s. The ratio of the mass of the rocket filled with fuel to its mass without fuel is R. Suppose R = 25, c = 2.8, and t = 100. Can the spacecraft attain a stable orbit 300 km above Earth?
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HW #53
8­6 P472 #1­4,7,10­12,14,15,17,18,20,24­26,29
Please put your name and class period at the top of
the homework. Also include the homework number.
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