Logarithm Calculator
Calculate natural log, common log, and logarithms with any base
Natural Logarithm
ln(x) - Base e ≈ 2.71828
ln(x) = logₑ(x)
Result:
0
Common Logarithm
log(x) - Base 10
log(x) = log₁₀(x)
Result:
0
Binary Logarithm
log₂(x) - Base 2
log₂(x)
Result:
0
Custom Base Logarithm
logᵦ(x) - Any base
logᵦ(x)
Result:
0
Antilogarithm
10ˣ - Inverse of log₁₀
antilog(x) = 10ˣ
Result:
0
Natural Exponential
eˣ - Inverse of ln
exp(x) = eˣ
Result:
0
Understanding Logarithms
What is a Logarithm?
A logarithm is the inverse operation of exponentiation. If by = x, then logb(x) = y.
logᵦ(x) = y ⟺ bʸ = x
Example:
2³ = 8, therefore log₂(8) = 3
10² = 100, therefore log₁₀(100) = 2
2³ = 8, therefore log₂(8) = 3
10² = 100, therefore log₁₀(100) = 2
Types of Logarithms
Natural Logarithm (ln):
Base e ≈ 2.71828 (Euler's number)
Base e ≈ 2.71828 (Euler's number)
ln(x) = logₑ(x)
Common Logarithm (log):
Base 10
Base 10
log(x) = log₁₀(x)
Binary Logarithm:
Base 2 (used in computer science)
Base 2 (used in computer science)
log₂(x)
Logarithm Properties
- Product Rule:
log(xy) = log(x) + log(y) - Quotient Rule:
log(x/y) = log(x) - log(y) - Power Rule:
log(xⁿ) = n·log(x) - Change of Base:
logᵦ(x) = log(x) / log(b) - Inverse Property:
log(bˣ) = x - Identity:
log(1) = 0andlog(b) = 1
Common Applications
- pH calculations in chemistry
- Earthquake magnitude (Richter scale)
- Sound intensity (decibels)
- Compound interest calculations
- Computer science algorithms
- Population growth models
- Signal processing
- Data compression
Copied!