Question

What is common logarithm or common log?

Answer 1

Hint: Logarithm is defined as inverse function of exponentiation. That means the logarithm of a number x is the exponent by which a fixed number y must be raised to give the number x. It is denoted by $ \log x $ . Common logarithm means the logarithm with base 10. For example, $ {\log _{10}}x $ . Properties and other important concepts of logarithms are discussed below.

Complete step-by-step answer:
Common logarithm is the logarithm with base 10. It is also known as decadic logarithm or decimal logarithm.
It is denoted as $ {\log _{10}}x $ .
Properties of logarithmic functions:
 $ \to $ Logarithm product rule: \[{\log _{10}}a + \log {}_{10}b = {\log _{10}}ab\].
 $ \to $ Logarithm quotient rule: \[{\log _{10}}a - {\log _{10}}b = \dfrac{{{{\log }_{10}}a}}{{{{\log }_{10}}b}}\].
 $ \to $ Logarithm power rule: \[{\log _{10}}{x^y} = y{\log _{10}}x\].
 $ \to $ Logarithm Base switch rule: \[{\log _y}x = \dfrac{1}{{{{\log }_x}y}}\].
Mantissa and Characteristics:
Mantissa is an important property of logarithms that makes calculations easier. The logarithm of a number greater than 1 that differs by a factor of a power of 10 have the same fractional part. This fractional part is known as mantissa.
 $ 1o{g_{10}}110 = {\log _{10}}\left( {{{10}^2} \times 1.1} \right) = 2 + {\log _{10}}\left( {1.1} \right) \approx 2 + 0.04139 = 2.04139 $
Here, the integer part that is 2 is called the characteristics.
Negative logarithms:
Negative logarithms means the value of logarithm of numbers less than 1.
 $ 1o{g_{10}}\left( {0.015} \right) = {\log _{10}}\left( {{{10}^{ - 2}} \times 1.5} \right) = - 2 + {\log _{10}}\left( {1.5} \right) \approx - 2 + 0.17609 = - 1.82391 $

Note: The numeric value of a logarithm with base 10 can be calculated with the following formula given below.
 $ {\log _{10}}x = \dfrac{{\ln x}}{{\ln 10}} $ .
Note that $ \ln $ and $ \log $ are different from each other. The difference between $ \ln $ and $ \log $ is that the base for $ \log $ is 10 and the base for $ \ln $ is e.