What is the Difference Between Log and ln?

The main difference between log and ln lies in the base they are defined for. Log is defined for base 10, while ln is denoted for base e (where e is an irrational and transcendental number approximately equal to 2.71828).

Here are the key differences between log and ln:

• Log:
• Logarithms are generally referred to as logarithms to the base 10.
• The exponential form for logarithms is 10^x = y.
• Logarithms are also known as common logarithms.
• Ln:
• Ln is also called the natural logarithm or logarithm of the base e.
• The exponential form for natural logarithms is e^x = y.
• Ln is the power to which the base 'e' must be raised to obtain a given value.

While both log and ln are logarithms, they are specific to different bases. Therefore, they are not exactly the same and cannot be used interchangeably in all cases. However, logarithms with base 10 can be adapted to work for base e, and vice versa, using the well-known relationship between exponentials and logarithms.

Comparative Table: Log vs ln

The main difference between log and ln lies in the base they use. Here is a table comparing the two:

Log generally refers to a logarithm to the base 10, also known as the common logarithm, and is represented as log10(x). On the other hand, ln refers to a logarithm to the base e, also known as the natural logarithm, and is represented as loge(x).