ICSE IX Maths Logarithms
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7/26/2019 ICSE IX Maths Logarithms
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ICSE IX ›› Maths ›› Logarithms
Logarithms
Complex mathematical problems with numerical expressions that involve multiplication and division of rational powers of
large numbers can be simplified by using logarithms and the laws related to it.
Consider:
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If ‘N’ and ‘a’ are any two positive real numbers, and for some real number ‘x’, ax = N, then ‘x’ is called the logarithm of ‘N’ to
the base ‘a’.
Please note that logarithms of only positive real numbers are defined. That is, ‘N’ must be greater than 0.
Here, ax = N is the exponential form, while x = logaN is the logarithmic form.
Consider: 42 = 16
In this exponential form, 4 is the base, 2 is the exponent, and 16 is the value.
Its logarithmic form will be:
Log416 = 2
Consider: log232 = 5
In this logarithmic form, 2 is the base, and the value of the logarithm is 5. The exponential form will be:
25 = 32
Some important results:
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IX Maths Logarithms http://www.learnnext.com/lesson/ICSE-IX-Maths-Logar
06/04/2013 0
7/26/2019 ICSE IX Maths Logarithms
http://slidepdf.com/reader/full/icse-ix-maths-logarithms 2/2
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A logarithm to the base 10 is called a common logarithm. Generally, the base as 10 in common logarithms is not
mentioned, and they are read as log 2, log 3, log 10, and so on. In other words, if the base is not mentioned, then the base
is considered as 10.
The laws of logarithms that help to solve complex calculations:
Logarithm of a product (Product Law):
Logarithm of a quotient (Quotient Law):
Logarithm of a power (Power Law):
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Lesson Summary
IX Maths Logarithms http://www.learnnext.com/lesson/ICSE-IX-Maths-Logar
06/04/2013 0