What is an antilogarithm?

An antilogarithm applies the inverse of a logarithm: for base b and exponent x, the result is b raised to x. For base 10 and exponent 3, the antilog is 1000, and log base 10 of 1000 is 3. Choose Power / antilog, enter the base and exponent, then calculate.

How do the linked inputs work?

Editing Exponent x selects the power direction. Editing Positive value y selects the logarithm direction. Calculate updates the other field with the unrounded floating-point result. Changing display precision affects the result text only and never feeds a rounded value into the linked calculation.

Which bases and inputs are valid?

The base must be finite, positive and different from 1. Bases between 0 and 1 are supported, as are zero and negative exponents. A real logarithm requires a positive argument. Complete decimal numbers and scientific notation are accepted. Infinity, NaN and trailing text are rejected.

How does change of base work?

The identity is log base b of y equals ln(y) divided by ln(b). Common bases use their corresponding browser logarithm functions, and a base close to 1 uses log1p to preserve precision. The calculation text shows the base logarithm and the inverse relationship. For base 2 and argument 8, the result is 3.

What does the inverse check establish?

The inverse reconstructs the original input using the other operation and reports its signed residual. The stated tolerance is 1e-12 times the larger of 1 and the absolute original input. This is a floating-point round-trip check, not symbolic proof. Near the smallest representable numbers, rounding may make the check fall outside tolerance; an overflowing or underflowing inverse is labelled unavailable.

What happens when a power is too large or too small?

A forward result that overflows the finite number range produces an explicit error. A positive mathematical power that underflows to floating-point zero also produces an error rather than presenting zero as exact. Finite subnormal results are retained with their inverse check. Values outside the real domain are not converted to complex numbers.

What do the graph and CSV contain?

The graph uses linear axes and a deterministic local interval around the current input. It marks the unrounded input point and samples the selected function at 201 coordinates. Samples outside the representable range remain gaps. The paged point table and CSV contain the actual coordinates, with unavailable values labelled rather than replaced by zero. The CSV includes the input point as a separate row.

Are my inputs uploaded or remembered?

Calculations, graphs and exports run locally without uploads. Edited valid numeric settings may be remembered under this tool's browser-storage key. Saved settings and the original example are labelled previews and do not count as a new calculation until you explicitly calculate. If clipboard access is blocked, the full calculation text remains selectable for manual copying.

Logarithm and Power Workbench

Link an exponent and its power for any positive base except 1. Switch between logarithms and antilogarithms, inspect an inverse check and explore the sampled curve with a point table and CSV export.

One relationship. Both directions.y = bˣ · x = logᵦ(y)

Choose the quantity to find

Base bPositive and different from 1. Bases between 0 and 1 are supported.

Exponent xInput for powerPositive value yUpdated by power

Display significant digits1 to 15 digits. Rounding changes display only.

Editing either x or y selects that direction. Calculation updates its inverse field with the unrounded value. Decimal and scientific notation are accepted.

Result and local curve

Calculate the linked pairThe result, inverse check and sampled curve appear together.

Edit either linked quantity, then calculate.

Direction: Power / antilog

Unrounded value: Not calculated

Display precision: Not calculated

Worked examples

AntilogarithmBase 10, exponent 3
10³ = 1000; log₁₀(1000) = 3.
LogarithmBase 2, argument 8
log₂(8) = 3; 2³ = 8.
Decreasing powerBase 0.5, exponent 3
0.5³ = 0.125.

Accuracy. Real-number floating-point results; overflow and values outside the real domain are explicit.

Common questions

What is an antilogarithm?: An antilogarithm applies the inverse of a logarithm: for base b and exponent x, the result is b raised to x. For base 10 and exponent 3, the antilog is 1000, and log base 10 of 1000 is 3. Choose Power / antilog, enter the base and exponent, then calculate.
How do the linked inputs work?: Editing Exponent x selects the power direction. Editing Positive value y selects the logarithm direction. Calculate updates the other field with the unrounded floating-point result. Changing display precision affects the result text only and never feeds a rounded value into the linked calculation.
Which bases and inputs are valid?: The base must be finite, positive and different from 1. Bases between 0 and 1 are supported, as are zero and negative exponents. A real logarithm requires a positive argument. Complete decimal numbers and scientific notation are accepted. Infinity, NaN and trailing text are rejected.
How does change of base work?: The identity is log base b of y equals ln(y) divided by ln(b). Common bases use their corresponding browser logarithm functions, and a base close to 1 uses log1p to preserve precision. The calculation text shows the base logarithm and the inverse relationship. For base 2 and argument 8, the result is 3.
What does the inverse check establish?: The inverse reconstructs the original input using the other operation and reports its signed residual. The stated tolerance is 1e-12 times the larger of 1 and the absolute original input. This is a floating-point round-trip check, not symbolic proof. Near the smallest representable numbers, rounding may make the check fall outside tolerance; an overflowing or underflowing inverse is labelled unavailable.
What happens when a power is too large or too small?: A forward result that overflows the finite number range produces an explicit error. A positive mathematical power that underflows to floating-point zero also produces an error rather than presenting zero as exact. Finite subnormal results are retained with their inverse check. Values outside the real domain are not converted to complex numbers.
What do the graph and CSV contain?: The graph uses linear axes and a deterministic local interval around the current input. It marks the unrounded input point and samples the selected function at 201 coordinates. Samples outside the representable range remain gaps. The paged point table and CSV contain the actual coordinates, with unavailable values labelled rather than replaced by zero. The CSV includes the input point as a separate row.
Are my inputs uploaded or remembered?: Calculations, graphs and exports run locally without uploads. Edited valid numeric settings may be remembered under this tool's browser-storage key. Saved settings and the original example are labelled previews and do not count as a new calculation until you explicitly calculate. If clipboard access is blocked, the full calculation text remains selectable for manual copying.

Real-number floating-point results; overflow and values outside the real domain are explicit.