Question

what are logarithms
explain about natural, common logarithms,characteristic, mantissa what are fundamental formulas



those who answer try to explain hugely it's for 12points keep in
mind

Answer 1

Hi friend,

LOGARITHMS:

a quantity representing the power to which a fixed number it means the base must be raised to produce a given number.so logarithim answers a question like this:
4 power?= 64

In this way:

4 power 3 = 64
log64 to base 4 = 64

the logarithm will tell us how the exponent is!

The general case is:

If a is a positive real number, other than 1 andam = x, then we write:
m = logax and we say that the value of log x to the base a is m.

* a power x = y

log y to base a = x

ex: log8 to the base 2 = 8

COMMON LOGARITHMS:

the logarithms which has base 10 is known as common logarithms.

ex: log100 to the base 10 = 2

log100 is it a common logarithm?

ans: yes, because if there is nothing in base there will be 10.so, log100 is a common logarithm.

NATURAL LOGARITHMS:

the logarithms which has base e is known as natural logarithm.


log 15 = 1.176= 1+0.176

CHARACTERISTIC:

In above 1 is characteristic.
the whole number or integral part of a logarithm, which gives the order of magnitude of the original number.

MANTISSA:

in above 0.176 is mantissa.
mantissa is part of a logarithm which is in decimal points.

FUNDAMENTAL FORMULAS:


1. loga (xy) = loga x + loga y

2. loga(x/y)= loga x - loga y

3. logx x = 1

4. loga 1 = 0

5. loga (xn) = n(loga x)

6. loga x =1logx a

7. loga x =logb x=log x.logb alog a


hope it helps.........

Answer 2

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