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Logarithm Calculator.

Evaluate a logarithm for any valid positive base and argument.

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01

Set your values

Results update as you type.

Result: 2

Result

2.000000
Natural log: 4.60517

Natural log

4.605170
Common log: 2

Common log

2.000000

Results update automatically as you type.

Use Cases

Solve exponential equations

Use logarithms to solve for unknown exponents in equations like 2^x = 16. Enter the argument (16) and base (2) to find x = 4.

Example: log_2(16) = 4

Convert between number systems

In computer science, logarithms with base 2 are used to determine the number of bits needed to represent a number. Enter the number as the argument and 2 as the base.

Example: log_2(256) = 8 bits

Frequently Asked Questions

How do I use the Logarithm Calculator?
Enter the argument (x) and the base (b) into the respective fields. The calculator will compute the logarithm of x with base b, i.e., log_b(x). Ensure that x > 0 and b > 0, b ≠ 1.
What is a logarithm?
A logarithm answers the question: to what exponent must the base be raised to produce a given number? For example, log_2(8) = 3 because 2^3 = 8. The calculator computes this value for any positive base and argument.
Can I use any base for the logarithm?
Yes, you can use any positive base except 1. Common bases include 10 (common log), e (natural log), and 2 (binary log). The calculator allows you to specify any base you need.

Tips & Common Mistakes

Tips

  • Ensure the argument (x) is greater than 0; logarithms of zero or negative numbers are undefined.
  • The base (b) must be positive and not equal to 1. Common bases like 10, e, and 2 are often used.
  • If you need the natural logarithm (base e), you can use the calculator with b = e (approximately 2.71828).
  • For quick mental checks, remember that log_b(1) = 0 and log_b(b) = 1 for any valid base.

Common Mistakes to Avoid

  • Entering a negative argument or zero, which is invalid because logarithms are only defined for positive numbers.
  • Using a base of 1, which is invalid because 1 raised to any power is always 1, so the logarithm would be undefined.
  • Confusing the argument and base: make sure you enter the number you are taking the logarithm of as 'x' and the base as 'b'.

Last updated: August 13, 2026