Logarithms
y = log10 x "Log to the base 10 of x equals y"
• Logarithms are exponents!
logbx = y This base
to this power
is equal to this.
by = x
Exponential Form
Logarithmic Form
23 = 8
log
10
100 = 2
4­2 = 1/16
log 81 = 4
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Example 1: Evaluate log1010,000
Example 2: Evaluate log .5 32
Example 3: Solve log3x = 4
Example 4: Solve logx(8/27) = 3
You Try!!
1. Evaluate log1/3 27
2. Solve logx(1/4) = 1/2
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The logarithm with base 10 is called the common logarithm. It is denoted by log10 or simply by log. The logarithm with base e is called the natural logarithm. It can be denoted by loge, but it is more often denoted by ln.
log 60 = log1060 this problem is really asking 10x = 60?
ln 0.1 = loge0.1 this problem is really asking ex = 0.1
SCIENCE CONNECTION The slope s of a beach is related to the average diameter d (in millimeters) of the sand particles on the beach by this equation:
s = 0.159 + 0.118 log d
Find the slope of a beach if the average diameter of the sand particles is 0.25 millimeter.
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HOMEWORK
PG. 503, #8­27 all, 58
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