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J.P.Sinha: Teacher of Physics and Maths for IIT-JEE and PMT

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LOGARITHM-1

LOGARITHM

Author: J.P.Sinha, a teacher of Physics, Maths for IIT-JEE/PMT


These days, logarithm has strangely been dropped from the school syllabus of CBSE-system. Thus depriving the students from learning a very important skill in mathematics. Logarithm is used to expedite the solution of complicated arithmetical calculations. It is also an important FUNCTION that gives useful formulae in Integration and Differentiation.

DEFINITION:

We know 2⁵=32 , so if we are asked 2^?=32 then obviously our answer will be 5.
When be write 2^?=32, we mean "to what power 2 must be raised to get 32?".
In mathematics normally we ask this question by using a different wording. We ask :
What is the logarithm of 32 to base 2?.And in symbols we express this question
as log₂ 32=?

Thus,

"to what power 2 be raised to give 32? ( i.e. 2^?=32)"
and
" what is the logarithm of 32 to base 2? (i.e. log₂ 32=?)"

are two different ways of asking the same thing.

So, whenever we write " log_a b =? " we mean "a^?=b".

And if, log_a b =c , then that will mean a^c=b.

The expression log_a b =c is read as " the logarithm of b to base a is c.

Now watch the following video that I have recorded to explain the basic idea Logarithm

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