This is a free lesson from our course in Algebra II
In this section you'll learn how to estimate values of logarithmic expression. Take a quick look at it. The system
of common logarithms has 10 as its base. When the base
is not indicated: log 100 = 2, then the system of common logarithms -base 10 - is
implied. You know 102 = 100 and its log form
is equivalent to log10100 = 2, and similarly 103 = 1000 and
its log form is equivalent to log101000 = 3. Therefore, log of any number
between 100 and 1000 to base 10 is 2 and 3 and such reasoning is helpful to evaluate
the value of logarithmic expressions.
For example, log105487 is between 3 and 4. You can say so as log105487=x 10x=5487 103=1000 & 104=10000.
As 5487 lies between 1000 & 10000,so we can say log105487 lies between 3 & 4.
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