Antilog Calculator

What does this antilog calculator compute?

The antilogarithm (antilog) is the inverse of a logarithm. If log_b(x) = y, then antilog_b(y) = b^y = x. Computing an antilog is the same as exponentiation.

The published formula or method is x = antilog_b(y) = bʸ. The following references support the stated mathematics or method:

• NIST DLMF §4.2 — Logarithm, Exponential, Powers: Definitions and mathematical identities for logarithms, exponentials, and powers.

Which inputs and limits should you check?

Follow the input domain, units, branch or solve direction, and rounding policy in the specification. Preserve exact outputs and any additional candidates or warnings.

The worked example uses Base 10 with 10³. Compare it with the Example calculations and the complete result for the same inputs.

How can you verify and cite this result?

CalculatorX is responsible for this page. The mathematical references above explain the model; implementation checks and their scope are documented separately in the math.antilog v1.0.7 Evidence and capability contract. Read the displayed verification and production state together with the specification's numerical limits.

Use the clean calculator URL to cite the tool. A shared input link identifies a particular calculation. Content updates, numerical verification, and domain reviews have separate dates and scopes.

What antilog means

A logarithm answers: “to what power must base b be raised to get x?”

y = log_b x

An antilogarithm undoes that step: raise the same base to y to recover x.

x = antilog_b(y) = b^y

So antilog is simply exponentiation — the inverse of log. Calculators rarely label a key “antilog”; they use 10^x, e^x, or y^x.

How to calculate antilog

1. Choose base b (default 10 if unspecified).
2. Enter the log value y.
3. Compute x = b^y.

Worked examples

Log vs antilog

Because they are inverses:

b^(log_b x) = x

log_b(b^y) = y

(for valid b and x).

Common, natural, and other bases

• Common antilog — base 10: x = 10^y. Inverse of the common logarithm, log₁₀(x), often written log(x).
• Natural antilog — base e ≈ 2.71828: x = e^y. Inverse of ln.
• Binary — base 2: useful in CS and information theory.
• Custom — any b > 0, b ≠ 1, including bases in (0, 1).

Characteristic and mantissa (optional background)

In traditional common-log tables, a logarithm is represented as an integer characteristic plus a non-negative fractional mantissa. For a positive example such as 2.6452, characteristic = 2 and mantissa = 0.6452. Tables looked up the mantissa to recover digits; magnitude came from the characteristic. Negative logarithms use a more involved table convention and are not expanded here. This tool skips tables and evaluates b^y directly.

Graph sketch (base 10)

Plotting this calculator’s input y against result x:

x = 10^y

• As y → −∞, x → 0⁺ (approaches the axis but never reaches it)
• As y → +∞, x grows exponentially
• At y = 0, x = 1

The same qualitative shape holds for any base b > 1. For 0 < b < 1, x = b^y decays as y increases.

Tips

• To remove a log from an equation, raise both sides to the log’s base (apply antilog).
• To remove an antilog, take log_b of both sides.
• Antilog of 0 is always 1 (b^0 = 1).
• Prefer the Log calculator or ln calculator when you need the forward transform; use Exponent for a general a^b pad.

CVP (Calculator Verification Protocol)

Math graph pilot under CVP 1.0 Proposed. Profile: core (unitless antilogarithm, not an engineering model).

• Evidence Manifest: /evidence/math.antilog/1.0.7.cvp.json
• Independent reference: O1 (model) + O3 mpmath/MPFR expected values and numerical behavior + O2 live identities
• Numerical policy: IEEE-754 binary64; ≤2 ULP vs O3; declared_before_evaluation=true
• Interfaces: UI (SSR), REST, and MCP must agree. A separate integration check covers URL → result → Live graph. ui-ssr is not a live browser session.
• Expert review is optional and is not required for CVP Verified.

Verified numerical and input contract

This calculator returns the positive finite binary64 scalar x = b^y. Selected decimal/scientific text is limited to512 characters; nonzero text that converts tozero rejects with NUMERIC_UNDERFLOW. Hexadecimal, nonfinite values, unknown fields and explicit blank or invalid bases reject. The input schemas expose validated display digits (default,4,6,10) and compare options; these do not change the numerical result.

Alias precedence: y then yInput; baseId then base; a selected explicit preset/numeric base takes precedence over b/baseInput; custom selects b then baseInput. With no base token, b then baseInput is selected; only a completely omitted base defaults to10. Nullish aliases fall through. Shadow values are ignored according to this order.

Symbolic e uses Math.exp(y), while numeric/custom bases use Math.pow with the normalized binary64 base. There is no proximity snapping. A result overflowing the finite range or rounding tozero is rejected; subnormal positive results are retained.51 independent Decimal150/250 references accept at most2ULP for these fixed vectors, alongside retained legacy O3 cases; this is not a guarantee across the whole domain or all runtimes.

Display digits control rounding, not additional computational precision. The inverse check uses unrounded x and is a consistency diagnostic, not independent verification. If x rounds to1 for nonzero y, inversion cannot recover the original exponent. For b near1 the forward result may round to1, and inverse recovery is sensitive to the small value ln(b); exponent perturbations scale with |y ln(b)|. Native CSV/JSON preserve the full scalar and raw provided input text.

Typing computes locally. Shared URLs send inputs to the server, and REST/MCP also receive inputs; URLs and requests may enter hosting or analytics logs. This review does not establish a retention/deletion guarantee or processing region.

Definitions: NIST DLMF §4.2. Independent reference arithmetic: Python decimal.