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 10^{2} = 100 and its log form
is equivalent to log_{10}100 = 2, and similarly 10^{3} = 1000 and
its log form is equivalent to log_{10}1000 = 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, log_{10}5487 is between 3 and 4. You can say so as log_{10}5487=x 10^{x}=5487 10^{3}=1000 & 10^{4}=10000.
As 5487 lies between 1000 & 10000,so we can say log_{10}5487 lies between 3 & 4.
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