Antilog Calculator – Antilogarithm
Recover a number from its logarithm using any positive base other than one.
How the result changes
Only logarithm base changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.
About this calculation
Antilog Calculator – Antilogarithm: Recover a number from its logarithm using any positive base other than one. Enter logarithm base, logarithm value; the reported quantities are antilogarithm. The equations and examples below show how those inputs lead to the result and where the model's assumptions matter.
Formula
antilog = base^exponent
Worked example
With Logarithm base: 10, Logarithm value: 2, antilogarithm is 100.
Method and inputs
The inverse of log base b is exponentiation with the same base: if log_b(x) = y, then x = b^y. Enter b and y, and raise the base to that power. This form excludes a base of exactly one because logarithms with that base are undefined.
Worked example
For base 10 and logarithm value 2, the antilogarithm is 10 squared, or 100. If the value is -2, the result is 0.01. With base 2 and value 3, the result would be 8 instead.
Check an antilog by taking the logarithm of the result with the original base. For example, log base ten of 100 is 2, which returns the example input. If that reverse check fails, the wrong base was probably selected, particularly when a scientific text alternates between log and ln.
How to read the result
A positive base raised to any real exponent gives a positive answer. A negative logarithm value does not imply a negative antilogarithm; it gives a fraction between zero and one when the base exceeds one. For a base below one, the direction reverses.
Fractional exponents produce roots: the antilog of 0.5 in base 9 is 3. A base between zero and one behaves differently from a base above one; raising 0.1 to 2 gives 0.01, while raising it to -2 gives 100. The equation remains valid in both cases.
Assumptions and checks
Real logarithms require the base to be positive and unequal to one. The calculator permits positive bases; a base of one will not represent an inverse logarithm, so choose a valid value before interpreting a result.
A common mistake is to calculate exponent^base instead of base^exponent. Another is using natural log values with base 10; the inverse of ln is e raised to the given value. Values with very large magnitude can overflow ordinary numeric precision.
Common questions
What does the antilog calculator – antilogarithm calculate?
It returns the positive number whose logarithm in the chosen base equals the entered logarithm value. The key operation is exponentiation, which undoes a logarithm taken with the same base.
When should I recalculate or check another method?
Recheck the original logarithm base whenever a textbook or data set gives only a log value. A calculator’s default log key often means base ten, while ln means base e; those yield very different inverse values.
Inputs
- Logarithm base
- Logarithm value