ICSE IX Maths Logarithms
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Library Home ICSE - IX (Change Class) Try Now for FREE Why Register? Full Name Full Name Email ID Email ID Country +91 Mobile Mobile By clicking the 'Join' button you agree to Terms & Conditions Already joined? Login here Lesson Summary Select subject 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: ⇒ If ‘N’ and ‘a’ are any two positive real numbers, and for some real number ‘x’, a x = 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, a x = N is the exponential form, while x = log aN is the logarithmic form. Consider: 4 2 = 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: 2 5 = 32 Some important results: ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ 502 Lo gi n| Si gn Up Home What is LearnNext? Free Trial Li brary Buy Blog FAQs Landline STD-Landline ICSE I X Maths Logarithms http://www.learnn ext.com/lesson/I CSE-I X-Mat hs-Logarit hms.htm 1 of 2 06/04/2013 06:52 PM
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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:
⇒
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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⇒
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
