Logarithm & Antilog Calculator Math

y = logb(x)
log10(10) = 1.000000

What is the Logarithm & Antilog Calculator?

Quick Answer: An interactive tool to compute logarithms and antilogarithms for any positive base. Enter a number and base, and instantly get the logarithm (exponent). Switch to antilog mode to find the number from its logarithm. The graph shows the logarithmic curve y = logb(x) with the current point highlighted.

Theory of Logarithms and Antilogs

The logarithm of a number x with base b is the exponent y such that by = x. Mathematically, y = logb(x). Common bases are 10 (common log), e (natural log, ln), and 2 (binary log). The antilogarithm is the inverse operation: given y, find x = by. The calculator uses JavaScript's Math.log (natural log) and converts using the change-of-base formula: logb(x) = ln(x) / ln(b). The graph plots y = logb(x) for x in (0, 100], with a moving cursor on the curve that updates as you adjust the input.

Step-by-Step Examples

Example 1: Common Log of 100

  1. Set mode to "Logarithm", base = 10, input = 100.
  2. Result: log10(100) = 2, because 102 = 100.
  3. The graph shows the point (100, 2) on the log curve.

Example 2: Natural Log (ln) of e

  1. Press the "e" preset, input = 2.71828.
  2. loge(e) = 1.

Example 3: Antilogarithm

  1. Switch to "Antilog" mode. Base = 10, input y = 3.
  2. Result: 103 = 1000. So antilog10(3) = 1000.
  3. The graph still shows the log curve, but the highlighted point corresponds to x = 1000, y = 3.

Frequently Asked Questions

What is the difference between log and antilog?

Log asks "b to what power equals x?" Antilog asks "what is b raised to power y?" They are inverse functions.

Why can't I take log of zero or negative numbers?

Logarithms are defined only for positive real numbers. The domain is (0, ∞). The tool restricts input to positive values.

How do I change the base?

Enter any positive number (except 1) in the base input. Use the presets for e, 10, or 2.

Is natural log the same as ln?

Yes, natural logarithm has base e ≈ 2.71828. In the calculator, set base = e.

Can I see intermediate steps?

The graph gives a visual representation. For step-by-step, you can use the formula logb(x) = ln(x)/ln(b) manually.