Example 1
- x = 1000
3
What is log₁₀(1000)? 3, because 10³ = 1000.
Log calculator
Type an x greater than zero. The common logarithm, log₁₀(x), asks what power of 10 returns x. log₁₀(1000) = 3, because 10³ = 1000. log₁₀(100) = 2. log₁₀(10) = 1.
The base is always 10. Another base, including e, lives on the logarithm card or the natural-log card. x ≤ 0 leaves a blank result.
Results
Enter data and click Calculate.
How it works
The common logarithm undoes a power of ten. You want the exponent y such that 10^y = x. For x = 1000 you get 3. For 100 you get 2. For 10 you get 1. For 1 you get 0, because 10⁰ = 1.
The calculator calls log₁₀. 20 is not a clean power of ten, so the result is a fraction, about 1.30103. 0.01 gives −2, because 10⁻² = 0.01. A minus in the result means x is a fraction smaller than 1, not that x is negative.
The field is x. Zero and negative numbers have no real logarithm. The calculator then stays blank. A comma and a dot are the same decimal. Type 1000 and click Calculate.
The natural logarithm ln uses base e, about 2.718. An arbitrary base lives on the logarithm card. Here ten is baked into the formula and there is no second field.
In decades and on the pH scale the same log₁₀ says how many zeros you moved away from 1. Three zeros after the one is 3. Two zeros is 2. This is not a percent and not a factorial.
log₁₀(1 000 000) = 6. log₁₀(0.1) = −1. log₁₀(50) ≈ 1.69897. log₁₀(2) ≈ 0.30103.
Formula
log₁₀(x) = Math.log10(x), for x > 0
How to use
- Type x, for example 1000.
- Click Calculate. log₁₀(1000) = 3.
- 100 gives 2. 10 gives 1. 1 gives 0.
- Zero and a minus leave a blank field.
- Base e lives on ln. Another base lives on the logarithm card.
log₁₀(1000) = 3
The common logarithm asks for a power of ten. log₁₀(1000) = 3. log₁₀(100) = 2. log₁₀(10) = 1. x must be positive.
- logarithm
- The inverse of a power. log₁₀(1000) = 3, because 10³ = 1000. Zero and a minus do not pass.
- log₁₀
- Logarithm base 10. log₁₀(10) = 1. log₁₀(1) = 0. Another base lives on another calculator.
- x
- The argument, a positive number. 1000 gives 3. 0.01 gives −2. Blank when x ≤ 0.
Examples
Example 2
- x = 100
2
What is log₁₀(100)? 2. Two zeros after the one.
Example 3
- x = 10
1
What is log₁₀(10)? 1. The base itself returns one.
Related calculators
Common questions
What is log₁₀(1000)?
3. 10³ = 1000. Each extra zero after the one adds 1 to the result.
What does common logarithm mean?
The exponent you raise 10 to in order to get x. Written log₁₀(x), or log(x) when the base ten is clear.
What are log₁₀(100) and log₁₀(10)?
2 and 1. log₁₀(1) = 0, because 10⁰ = 1.
Do 0 and negative numbers pass?
No. A real logarithm needs x > 0. The result is a blank result.
What is log₁₀(0.01)?
−2. 10⁻² = 0.01. The minus says x is a fraction, not that you typed a negative x.
How is this different from ln?
ln has base e. Here the base is 10. Another number, the same question about an exponent.
Where do I change the base?
On the logarithm card you type the base yourself. Here ten is fixed.
What is log₁₀(20)?
About 1.30103. 20 is not a clean power of 10, so the result is not a whole number.
Does a comma in 0.1 work?
Yes. 0.1 and 0,1 both give −1. That is 10⁻¹.
Why log₁₀ in pH?
pH is minus the log of a concentration. Plain log₁₀(x) is what you compute here, with no chemistry in the field.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.