How this instrument works
An antilogarithm undoes a logarithm. If log base b of some number y equals x, then the antilog of x in that same base recovers y, and it does so by the plainest route possible: raise the base to the power x. There is no separate machinery here — antilog_b(x) is defined as b raised to x, full stop. The name only exists because, before calculators, people needed a word for the step that reverses a log-table lookup.
That history explains why the operation still carries a distinct name instead of just being called exponentiation. Nineteenth and early twentieth century engineers multiplied large numbers by adding their logarithms, read off a log table, then looked the sum back up in an antilogarithm table to get the answer — the same trick a slide rule performs mechanically by sliding two logarithmic scales and reading the antilog off a third. Addition of logs became multiplication of the original numbers precisely because antilog_b(p + q) equals antilog_b(p) times antilog_b(q).
Because a positive base raised to any real power never touches zero and never turns negative, the antilog curve stays entirely above the horizontal axis no matter how negative x becomes — it only creeps closer to zero without ever reaching it. That single fact rules out a negative or zero result from this sheet for any real logarithm value you enter, which is a useful check against a typo in the Base field.
- Enter the number you want to reverse a logarithm for into Logarithm value, x — this is the exponent, not the original number.
- Set Base to the same base the original logarithm used; base ten is the common choice, base e gives the natural antilog.
- Read Antilog (baseˣ) for the recovered number: base raised to the power x.
- Try x = 0 to see every base return exactly 1, and a negative x to see a result between 0 and 1.
Worked example — reversing log₁₀(100) = 2
Set Base to 10 and Logarithm value, x to 2. Antilog (baseˣ) returns 10 raised to the power 2, which is 100.0. This is the mirror image of the familiar fact that log₁₀(100) = 2: since ten squared is a hundred, the antilog of 2 in base ten is a hundred. Start from either side of that equation and you land on the same pair of numbers, 2 and 100, joined by the same relationship read in opposite directions.
Two more settings show the shape of the curve either side of that anchor. Drop Logarithm value, x to 0 and Antilog returns 1 exactly, because any positive base raised to the zeroth power equals 1 — the one point every antilog curve shares regardless of base. Set x to −1 instead and Antilog returns 0.1, since ten to the power −1 is one tenth: a negative logarithm value always yields a result strictly between 0 and 1, never a negative number.
Questions
What does antilog actually mean?
It means reversing a logarithm. If log base b of y equals x, the antilog of x in base b gives back y — computed as b raised to the power x. The two operations are inverses of the same relationship, the way squaring and taking a square root undo each other.
Isn't antilog just the same thing as raising a number to a power?
Arithmetically, yes — antilog_b(x) is defined as b^x, nothing more. The separate name survives from log-table and slide-rule days, when 'take the antilog' was the specific final step that converted an added-up logarithm back into an ordinary number.
Why does the antilog of 0 always equal 1?
Because any positive base raised to the power 0 equals 1 by the basic rule of exponents, regardless of what that base is. It is the one input where every antilog curve, base 2, base 10, or base e, passes through the same point on the vertical axis.
Can an antilog ever come out negative or zero?
Not for a positive base. A positive number raised to any real power stays positive, so the result only shrinks toward zero as the logarithm value grows very negative — it never reaches zero and never crosses into negative territory.
How were antilogarithms used before calculators existed?
Engineers added two numbers' logarithms, read the sum, then looked up its antilog to get the product — turning multiplication into addition. A slide rule automates the same trick mechanically, sliding logarithmic scales and reading the antilog off a fixed one.
What is the difference between a common antilog and a natural antilog?
A common antilog uses base 10, the traditional choice for log tables. A natural antilog uses base e ≈ 2.71828 and is identical to the exponential function exp(x). Enter 10 or 2.71828 in the Base field to get either one from this same sheet.