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.