Difference Between Log and Ln

The difference between log and ln is that log is defined for base 10 and ln is denoted for base e. For example, log of base 2 is represented as log2 and log of base e, i.e. loge = ln (natural log).

Log

• Log refers to a logarithm to the base 10
• This is also called as a common logarithm
• The common log is represented as log10 (x)
• The exponent form of the common logarithm is 10x =y
• The interrogative statement for the common logarithm is “At which number should we raise 10 to get y?”
• It is more widely used in physics when compared to ln
• Mathematically, it is represented as log base 10

Ln

• Ln refers to a logarithm to the base e
• This is also called as a natural logarithm
• The natural log is represented as loge (x)
• The exponent form of the natural logarithm is ex =y
• The interrogative statement for the natural logarithm is “At which number should we raise Euler’s constant number to get y?”
• As logarithms are usually taken to the base in physics, ln is used much lesser
• Mathematically, this is represented as log base e