Download 8-4 Properties of Logarithms

8-4 Properties of Logarithms
 Check Skills You’ll Need
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Properties of Logarithms
PRODUCT
QUOTIENT
POWER
log b MN  log b M  log b N
M
log b
 log b M  log b N
N
x
log b M  x log b M
Loudness of Sounds
Decibels
I
L  10 log
I0
I is the intensity of the sound wave in watts per square meter.
I0 is the lowest-intensity sound that the average human ear can detect.
Noise Control
 L1 = present loudness
 L2 =reduced loudness
 I1 = present intensity
L1 – L2 is how much the
loudness changed.
 I2 = reduced intensity
I1
I2
L1  L2  10 log  10 log
I0
I0
8-5 Exponential and Logarithmic
Equations
 Taking the log of both sides of an equation.
 Change of Base formula.
 If an equation is in exponential form, then
take the log of both sides.
 If an equation is in logarithmic form, then
write it in exponential form.
 Don’t forget to use the properties.
Intentionally blank
8-6 Natural Logarithms
 Remember e.
 The function y = ex has an inverse, THE NATURAL
LOGARITHMIC FUNCTION.
ye
x
log e y  x
ln y  x
Properties
 All of the properties of common logarithms
apply to natural logarithms also.