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Log (Logarithm) Calculator

Compute a logarithm in any base — natural, base 10, base 2 or a custom base — using the change-of-base formula.

Related tools

All Algebra & equations tools →
Natural Log CalculatorCompute ln(x), the natural logarithm in base e, to the number of decimal places you choose.Antilog Calculator (inverse logarithm)The antilogarithm undoes the logarithm: antilog_b(y) = bʸ, so log_b(bʸ) = y. Pick base 10, e, 2 or your own, enter the exponent, and the result comes back with the inverse relationship spelled out and the round trip checked. Bases of zero or less, and base 1, are rejected with the reason.Log Base 10 CalculatorCompute log₁₀(x) for a single value, a whole list at once, or invert it to find x from a known logarithm.Log Base 2 CalculatorCompute log₂(x) for any positive number, with exact results flagged for powers of two.Absolute Value Equation SolverSolve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions.Absolute Value Inequality SolverSolve absolute-value inequalities such as |x+3| < 5 or |x−2| > 3 and get the solution as an interval, with AND/OR reasoning explained step by step.Algebraic Expression SimplifierCombines like terms, expands or factors, with implicit multiplication understood (2x is 2·x). When a cancellation removes a factor, the excluded value is stated — (x²−4)/(x−2) is x+2 only for x ≠ 2, and that restriction is part of the answer.Beta Function CalculatorCompute the Euler Beta function B(x, y) = Γ(x)·Γ(y) / Γ(x+y) via a stable log-gamma.

Open Log (Logarithm) Calculator and you get an answer straight away, with no account to create. It sits under Algebra & equations in our catalogue, alongside Natural Log Calculator and Antilog Calculator (inverse logarithm).

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Log (Logarithm) Calculator do?

Compute a logarithm in any base — natural, base 10, base 2 or a custom base — using the change-of-base formula.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Log (Logarithm) Calculator different from Natural Log Calculator?

They sit next to each other but answer different questions: Natural Log Calculator is the one to open when you need it to compute ln(x), the natural logarithm in base e, to the number of decimal places you choose. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Antilog Calculator (inverse logarithm) is the closest one after this: The antilogarithm undoes the logarithm: antilog_b(y) = bʸ, so log_b(bʸ) = y. Pick base 10, e, 2 or your own, enter the exponent, and the result comes back with the inverse relationship spelled out and the round trip checked. Bases of zero or less, and base 1, are rejected with the reason.

What else is worth having open alongside it?

Log Base 10 Calculator and Log Base 2 Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
ExplainerHow Half-Life Works: What Is Left After 1, 3 and 10 Half-LivesOne half-life leaves 50%, three leave 12.5%, ten leave less than a tenth of a percent. The formula is a single line — the part worth understanding is why the answer never reaches zero.How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.