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Calculation Machine

Logarithm Calculator

log base 10, natural log and any custom base at once.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
log base 5
4.29203
log₁₀ (common log)
3
ln (natural log)
6.907755
log₂ (binary log)
9.965784
Exponent form
5^4.292 = 1000
Antilog check (10^log₁₀x)
1000

Quick answer

log_b(x) answers the question 'b to what power gives x?' — so log₁₀(1000) = 3 because 10³ = 1000.

The formula

log_b(x) = ln(x) ÷ ln(b)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Value x1000
  • Custom base b5

Result

  • log base 54.29203
  • log₁₀ (common log)3
  • ln (natural log)6.907755
  • log₂ (binary log)9.965784
  • Exponent form5^4.292 = 1000
  • Antilog check (10^log₁₀x)1000

How to use the Logarithm Calculator

  1. 1Enter the number you want the logarithm of — it must be positive.
  2. 2Enter any custom base you need.
  3. 3Compare all four bases at once, or copy the exponent form for your working.

Frequently asked questions

Why can't I take the log of a negative number?

No real power of a positive base gives a negative result, so real logs are defined only for positive inputs.

What is log(1)?

Zero in every base, because any base raised to the power 0 equals 1.

About this calculator