Calculate antilog, pH or pOH, and logarithm values in base 10, e, 2, or custom base, including hydrogen and hydroxide ion concentrations at 25°C.
Inverse Log Formula
The inverse of a logarithm is an exponent. If you know the log value, raise the base to that power to recover the original number.
x = b^y
- x = original number (the antilog)
- b = base of the logarithm
- y = the log value you start with
For pH and pOH, the calculator uses the same idea with base 10 and a negative sign:
[H+] = 10^(-pH) [OH-] = 10^(-pOH)
The Log tab runs the calculation in reverse, solving y = logb(x). Base must be greater than 0 and not equal to 1. For the Log tab, x must be greater than 0.
Common Bases and Quick Reference
The three bases you will see most often:
| Base | Name | Inverse Form | Typical Use |
|---|---|---|---|
| 10 | Common log | x = 10^y | pH, decibels, Richter scale |
| e ≈ 2.71828 | Natural log | x = e^y | Growth, decay, calculus |
| 2 | Binary log | x = 2^y | Computing, information theory |
For the pH tab, the result tells you whether the solution is acidic, neutral, or basic at 25°C:
| pH Value | [H⁺] (mol/L) | Classification |
|---|---|---|
| 1 | 1 × 10⁻¹ | Strong acid |
| 4 | 1 × 10⁻⁴ | Weak acid |
| 7 | 1 × 10⁻⁷ | Neutral |
| 10 | 1 × 10⁻¹⁰ | Weak base |
| 13 | 1 × 10⁻¹³ | Strong base |
Worked Examples
Example 1: Antilog base 10. Given y = 3, find x.
x = 10³ = 1000.
Example 2: Antilog base e. Given y = 2, find x.
x = e² ≈ 7.389.
Example 3: pH to concentration. Given pH = 4.5, find [H⁺].
[H⁺] = 10⁻⁴·⁵ ≈ 3.16 × 10⁻⁵ mol/L.
Example 4: Log of a number. Given x = 1000, base 10.
y = log₁₀(1000) = 3.
FAQ
Is "inverse log" the same as "antilog"? Yes. Both refer to raising the base to the power of the log value.
Why can't the base equal 1? 1 raised to any power equals 1, so the function has no inverse at that base.
Can the log value be negative? Yes. A negative y produces a result between 0 and 1. For example, 10⁻² = 0.01.
Can x be negative in the Log tab? No. Logarithms of zero or negative numbers are undefined for real bases.
