Log Calculation

1. Select the logarithm formula you want to find.
2. Enter the numbers needed for the calculation: base (b) and variable (x).
3. The logarithm calculation result will be calculated automatically.

"Log" is an abbreviation for logarithm, a mathematical function that shows how many times a number is multiplied by a specific base (b) to get another number (x). Specifically, it is defined as follows:

Definition of logarithm

Here, "b" is the base, "x" is the number or variable to take the logarithm of, and "n" is the result.

Main types of logarithms

• Natural logarithmln(x)Logarithm to base 10
• Common logarithmlog₁₀(x)Logarithm to Napier's constant (approximately 2.718)
• log_b(x)Logarithm to any base

How to calculate logarithm

A logarithm tells you how many times you need to multiply a number by a specific base to get a given number. It is expressed as follows:

Definition:
log_b(a) = c is b^c = a.

Main types of logarithms

• Natural logarithm: ln(x) (base e)
• Common logarithm: log₁₀(x) (base 10)
• Logarithm in any base: log_b(x)

Calculation method

1. Logarithm conversion formula:
   log_b(a) = log_k(a) / log_k(b)
2. Calculation procedure:
   • Divate the given number (a) by the base (b) to calculate the required logarithm.
   • Use a calculator to find the natural or base 10 logarithm.

Example

log₂(16) = log₂(2⁴) = 4

This tool is available for free.