This is a free lesson from our course in Algebra II
This lesson explains how to use the
laws of logarithm discussed earlier for simplifying logarithmic
equations and apply these for solving the
assorted word problems. To begin with it may require some patience
to understand but hen you walk through some examples with solution,
and the instructor's
explanation with the help of audio, video presentation
and in own hand writing,
you find it much simpler. Generally logarithmic word problems involve evaluating
a given
logarithmic equation at a given point, and solving for a given
variable. E.g. if the intensity of a gunshot is expressed by equation I
= (2.5 x 10^{13})I_{0} and noise level D_{b}(decibels) is
given by 10log[ I
I_{0} ], the later equation yields noise level of about 134 decibels.
(More text below video...)
(Continued from above) But
exponential word problems almost always work for the growth / decay formula:
A = Pe^{rt}
Where "A"; is the quantity at the end, "P"; is the quantity in the beginning,
"r" is the growth or decay rate, and "t"; is time.
For example, in a research project the growth rate constant; for species of 100
bacteria in the beginning (after 6 hours multiplies to 450), will be 0.25/hour. There are a number of rules which enable us to rewrite expressions involving logarithms in different,yet equivalent, ways. These rules are known as the laws of logarithms.. All the laws of logarithms flow directly out of the laws of exponents. The laws apply to logarithms of any base but the same base must be used throughout a calculation.
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