Enter any positive number (x) into the Log Base 10 Calculator and get the common logarithm (log₁₀(x)) — the power to which 10 must be raised to equal your number. You also see the equivalent natural log (ln) and log base 2 values side by side. Great for science, engineering, pH calculations, decibel levels, and Richter scale problems.
log₁₀(x)
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Natural Log ln(x)
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Log Base 2 log₂(x)
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Inverse: 10^y equals
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Log base 10, also called the common logarithm and written as log₁₀(x) or simply log(x), is the power to which 10 must be raised to produce a given number. For example, log₁₀(1000) = 3 because 10³ = 1000. It is widely used in science, engineering, and everyday measurements like the pH scale and decibel levels.
It is called the common logarithm because base 10 aligns naturally with our decimal number system, making it the most commonly used logarithm in practical applications. Before calculators existed, base-10 logarithm tables were the standard tool for complex multiplications and divisions in science and engineering.
To calculate log₁₀(x), you find the exponent y such that 10^y = x. In JavaScript (and most programming languages) this is computed as Math.log10(x) or equivalently Math.log(x) / Math.log(10). For example, log₁₀(100) = 2 and log₁₀(0.01) = -2.
The domain of log base 10 is all positive real numbers (x > 0). Logarithms are undefined for zero and negative numbers in the real number system. As x approaches 0 from the positive side, log₁₀(x) approaches negative infinity.
log₁₀(1) = 0 for any base, because any number raised to the power of 0 equals 1. In other words, 10⁰ = 1, so the common logarithm of 1 is always 0.
Yes. log₁₀(x) is negative whenever 0 < x < 1. For instance, log₁₀(0.01) = -2 because 10⁻² = 0.01. The logarithm of a number between 0 and 1 is always negative, and the input itself must still be positive.
log (common logarithm) uses base 10, while ln (natural logarithm) uses base e ≈ 2.71828. In scientific and engineering contexts 'log' typically means base 10, whereas in pure mathematics 'log' sometimes implies the natural logarithm. The two are related by the formula: ln(x) = log₁₀(x) × ln(10) ≈ log₁₀(x) × 2.302585.
Log base 10 appears in many real-world measurement scales. The pH scale measures acidity (pH = -log₁₀[H⁺]), the Richter scale measures earthquake magnitude, and the decibel scale measures sound intensity — all using base-10 logarithms. It is also used in astronomy, finance (compound growth), signal processing, and data compression.