How do I use the Log Calculator?

Enter the required values, then calculate. The Log Calculator shows results, formulas, and step-by-step work when available. No account is required.

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How it works

log_b(x) = y means b^y = x. Use change of base log_b(x) = ln(x)/ln(b). Base e is ln; base 10 is common log; base 2 is binary log.

log_b(x) = y ⇔ b^y = x

When to use

Use this tool when you need to: leave one field blank. Type e for natural log. Example: base 2, argument 8 → 3.

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Leave one field blank. Type e for natural log. Example: base 2, argument 8 → 3.

Frequently asked questions

What is the Log Calculator?: log_b(x) = y means b^y = x. Use change of base log_b(x) = ln(x)/ln(b). Base e is ln; base 10 is common log; base 2 is binary log.
How do I use the Log Calculator?: Enter the required values, then calculate. The Log Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Log Calculator use?: log_b(x) = y ⇔ b^y = x

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Logarithm calculator

Provide any two values in log_b(x) = y to find the third. Base may be e (natural log), 10, 2, or any valid number; fractions accepted.

How it works

What is a logarithm?

The logarithm is the inverse of exponentiation. The log of a number is the power a fixed base must be raised to in order to yield that number. If x = b^y, then y = log_b(x), where b is the base. Conventionally, log means base 10. When the base is e, we write ln rather than log_e. log₂ (binary logarithm) is common in computer science. Base 10 is used in science and engineering; base e in math and physics.

Basic log rules

Product: log_b(x · y) = log_b(x) + log_b(y) EX: log(1 · 10) = log(1) + log(10) = 0 + 1 = 1 Quotient: log_b(x / y) = log_b(x) − log_b(y) EX: log(10 / 2) = log(10) − log(2) ≈ 0.699 Power: log_b(x^y) = y · log_b(x) EX: log(2^6) = 6 · log(2) ≈ 1.806

Change of base

On any calculator that supports ln or log₁₀: log_b(x) = log_k(x) / log_k(b) = ln(x) / ln(b) = log₁₀(x) / log₁₀(b) EX: log₂(8) = ln(8)/ln(2) = 3 To swap base and argument: log_b(c) = 1 / log_c(b) EX: log₅(2) = 1 / log₂(5)

Common values

log_b(1) = 0 log_b(b) = 1 log_b(0) is undefined lim_(x→0⁺) log_b(x) = −∞ (for b > 1) ln(e^x) = x

Related calculators

Scientific and exponent tools work with the same exponential–logarithm relationship; half-life and roots use related power math.

How it works

log_b(x) = y means b^y = x. Use change of base log_b(x) = ln(x)/ln(b). Base e is ln; base 10 is common log; base 2 is binary log.

log_b(x) = y ⇔ b^y = x

When to use

Use this tool when you need to: leave one field blank. Type e for natural log. Example: base 2, argument 8 → 3.

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Leave one field blank. Type e for natural log. Example: base 2, argument 8 → 3.

Frequently asked questions

What is the Log Calculator?: log_b(x) = y means b^y = x. Use change of base log_b(x) = ln(x)/ln(b). Base e is ln; base 10 is common log; base 2 is binary log.
How do I use the Log Calculator?: Enter the required values, then calculate. The Log Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Log Calculator use?: log_b(x) = y ⇔ b^y = x

Browse categories