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