What Is a Log Calculator?
A log calculator is a free online tool that computes logarithms of any base — instantly and with step-by-step solutions. While a basic calculator only has LOG (base 10) and LN (natural log) buttons, our online log calculator goes much further: it calculates log with any custom base using the change-of-base formula, computes the inverse log (antilog), handles negative logs, and even solves log equations where you provide two values and find the third.
What Does Log Mean on a Calculator?
LOG Button = Log Base 10 (Common Logarithm)
The LOG button on a calculator computes the base-10 logarithm. It answers: "To what power must I raise 10 to get this number?"
log₁₀(x) = y means 10^y = x
📘 Examples — What is log on a calculator?
log(10) = 1 → because 10¹ = 10
log(100) = 2 → because 10² = 100
log(1000) = 3 → because 10³ = 1000
log(0.1) = −1 → because 10⁻¹ = 0.1
log(50) ≈ 1.699 → because 10^1.699 ≈ 50
LN Button = Natural Logarithm (Base e)
The LN button computes the natural logarithm — logarithm with base e (Euler's number ≈ 2.71828). It answers: "To what power must I raise e to get this number?"
ln(x) = y means eʸ = x
Online log calculator — compute log₁₀, ln, custom base, inverse log instantly with steps
How to Use Log on a Calculator — All Methods
Method 1: Log Base 10
Select the Log₁₀ tab, enter your number (x), and click Calculate. The result is log₁₀(x).
Method 2: Natural Log
Select the ln tab, enter your number, and click Calculate. Returns logₑ(x) = ln(x).
Method 3: Log with Any Base (Change of Base Formula)
Select Custom Base, enter the value and base. The calculator uses the change-of-base formula:
log_b(x) = log(x) / log(b) = ln(x) / ln(b)
📘 Example — How to type log base 2 in a calculator
log₂(32) = log(32)/log(2) = 1.5051/0.3010 = 5
Verify: 2⁵ = 32 ✓
log₃(81) = log(81)/log(3) = 1.9084/0.4771 = 4
Verify: 3⁴ = 81 ✓
Method 4: How to Do Inverse Log on a Calculator
The inverse log (antilog) reverses a logarithm. If log₁₀(x) = y, then antilog(y) = 10^y.
antilog₁₀(y) = 10^y
Select the Inverse Log tab, enter the log value and base. The calculator computes b^y.
📘 Example — Inverse Log
antilog(3) base 10 = 10³ = 1000
antilog(0.699) base 10 = 10^0.699 ≈ 5
antilog(2) base e = e² ≈ 7.389
How to change log base on a calculator: On physical calculators, use the change-of-base formula: log_b(x) = LOG(x) ÷ LOG(b). On our online log calculator, simply select the Custom Base tab — it applies the change-of-base formula automatically and shows you the working.
Negative Log Calculator — How It Works
A negative log simply means the logarithm of a number between 0 and 1. For example:
- log(0.1) = log(10⁻¹) = −1
- log(0.01) = log(10⁻²) = −2
- log(0.001) = log(10⁻³) = −3
In chemistry, pH = −log[H⁺] — so a negative log gives a positive pH value. Enter any number between 0 and 1 in our Log Base 10 mode to get a negative log result automatically.
Logarithms in real life — pH, decibels, Richter scale, compound interest, and algorithm complexity
Log Base 2 — Used in Computer Science
Log base 2 (binary logarithm) is fundamental in computer science and information theory. It answers: "How many times must I double 1 to reach this number?"
- log₂(2) = 1 — 1 bit can represent 2 values
- log₂(8) = 3 — 3 bits for 8 values (0–7)
- log₂(256) = 8 — 8 bits for 256 values (one byte)
- log₂(1,048,576) = 20 — 20 bits for ~1 million values
Use our Custom Base mode with base = 2 for any binary logarithm calculation.
