Logarithms

The rules of logarithms - log10 and loge for numbers ranging 1 to 1000. Calculate logarithms to different bases (base 10, base e, base 2) and explore logarithmic conversions.

Number (x)log₁₀(x)logₑ(x) [ln(x)]log₂(x)
1000
20.3010.69311
50.6991.60942.3219
1012.30263.3219
501.6993.9125.6439
10024.60526.6438
5002.6996.21468.9658
100036.90789.9657
Calculator

Inputs

Results

log₁₀(x)--
logₑ(x) [ln(x)]--
log₂(x)--
Convert ln(x) to log₁₀(x)--
Convert log₁₀(x) to ln(x)--

Logarithmic Rules

  1. Product Rule: log_a(xy) = log_a(x) + log_a(y)
  2. Quotient Rule: log_a(x/y) = log_a(x) - log_a(y)
  3. Power Rule: log_a(x^p) = p·log_a(x)
  4. Reciprocal Rule: log_a(1/x) = -log_a(x)
  5. Base Rule: log_a(a) = 1
  6. Unity Rule: log_a(1) = 0

Conversion Formulas

  • log₁₀(x) = 0.434294 × ln(x)
  • ln(x) = 2.302585 × log₁₀(x)
  • log₂(x) = 1.442695 × ln(x) = 3.321928 × log₁₀(x)