Logarithmic Functions

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Logarithmic Functions
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Example1. On the Richter Scale, the magnitude R
of an earthquake of intensity I is given by
where I0 is a certain minimum intensity.
If the intensity of an earthquake is 1000I0 Find
R.
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Example1. The Richter Scale,
If the intensity of an earthquake is 1000I0
Find R.
R 3
R log 1000
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Example2. On the Richter Scale, the magnitude R
of an earthquake of intensity I is given by
where I0 is a certain minimum intensity.
Express I in terms of R and I0
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Example2. The Richter Scale,
10R I/I0
I I0 10R
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Example3.
Newton law of cooling states that the rate at
which an object cools is directly proportional
to the difference in temperature between the
object and its surroundings.
The temperature T if an object at time t is
given by T 75 e-2t .
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Example3.
The temperature T if an object at time t is
given by T 75 e-2t .
Express t as a function of T.
T 75 e-2t
e-2t T/75
-2t ln T/75