Change of Base Formula Calculator

Your details

The number inside the logarithm. Must be positive (greater than zero).
The current base of the logarithm. Must be positive and not equal to 1.
The base to convert to. Most scientific calculators natively support base 10 and base e.
logₐ(x)
3

The evaluated value of the original logarithm

Numerator logᵇ(x)0.90309
Denominator logᵇ(a)0.30103
Verification: a^result8
Numerator log_b(x)0.90309
Denominator log_b(a)0.30103
Result log_a(x)3

log_2(8) = 3.000000

  • log_2(8) = 3.000000, meaning 2 raised to the power 3.0000 equals 8.
  • You can now evaluate this on any scientific calculator using the log key: log(8) / log(2).
  • The result is the whole number 3, so 2^3 = 8 is an exact relationship.
  • The numerator (0.9031) is the common log (base 10) of 8; the denominator (0.3010) is the common log (base 10) of 2. The ratio gives the original logarithm.

Next stepTo verify on a calculator: enter log(8) divided by log(2) for base 10, or ln(8) divided by ln(2) for the natural log. Both give the same answer.

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