Free · Exponents and logarithms

Antilog & Logarithm with a Chosen Base

Convert a logarithm value back to its number with a positive base, or recover the logarithm from the number.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

With base 10, the antilog of 3 is 1,000 because 10³ = 1,000. With base 2, the antilog of 3 is 8. Always use the same base as the original logarithm.

y = b^x; x = ln(y) / ln(b)

Worked example

Enter these known values and leave the other values blank.

Logarithm base b
10
Logarithm value x
3
Original number y = b^x
1000

Assumptions and limitations

  • The real logarithm base must be positive and different from 1. Bases between 0 and 1 are supported and reverse the direction of growth.
  • The base begins at 10 and is locked for reverse solving. You can edit it; unlock it only when you intend the calculator to solve for the base.
  • The logarithm value may be positive, negative or zero. A value of zero gives antilog 1 for every allowed base.
  • When x is zero and y is 1, the base is not uniquely determined. Keep a chosen base entered for that case.
  • Finite precision and display rounding apply to noninteger powers and logarithms.

Common questions

Is an antilog the same as a reciprocal?

No. Antilog reverses a logarithm by raising its base to the logarithm value. A reciprocal divides one by a number.

Can the antilog result be negative?

For the real logarithms used here, the result is strictly positive. A negative logarithm value gives a positive result less than 1 when the base exceeds 1.

References

Bookify requires a positive logarithm base other than one and a strictly positive antilog result.

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