Logarithm Calculator
Calculate natural logarithm, common logarithm, and custom base logarithms with step-by-step solutions
📊 Logarithm Calculator
Quick Examples:
- • log₁₀(100) = 2
- • ln(e) = 1
- • log₂(8) = 3
- • antilog(2) = 10² = 100
Formula
log(x) = log₁₀(x)
Where:
- x =Input value
- b =Base of logarithm
- e =Euler's number (≈ 2.71828)
- ln =Natural logarithm (base e)
- log =Common logarithm (base 10)
About Logarithms
A logarithm is the power to which a base must be raised to produce a given number. It's the inverse operation of exponentiation.
Types of Logarithms:
- • Common (log): Base 10, used in engineering
- • Natural (ln): Base e, used in calculus
- • Binary (log₂): Base 2, used in computer science
- • Custom Base: Any positive base ≠ 1
Key Properties:
- • log_b(xy) = log_b(x) + log_b(y)
- • log_b(x/y) = log_b(x) - log_b(y)
- • log_b(x^n) = n × log_b(x)
- • log_b(b) = 1, log_b(1) = 0
Applications:
- • pH calculations in chemistry
- • Decibel measurements in acoustics
- • Earthquake magnitude (Richter scale)
- • Algorithm complexity analysis