Algebra
Logarithm Calculator
Evaluate log, ln, and log base n of any number. Calculate common log (base 10), natural log (base e), and custom base logarithms with change-of-base working shown.
Examples:
Formula Reference
Linear Equation
ax + b = c → x = (c−b)/a
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Discriminant
Δ = b² − 4ac
Vertex Form
y = a(x−h)² + k
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Solution Methodology
01
Enter Value & Base
Provide x and the desired base (10, e, or custom n).
02
Apply Change of Base
Compute logₙ(x) = ln(x)/ln(n) showing each ln evaluation.
03
Display Antilog
Show the inverse: if logₙ(x) = y, then x = nʸ for verification.
Common Questions
What is the change-of-base formula for logarithms?
logₙ(x) = log(x)/log(n) = ln(x)/ln(n). This allows any logarithm to be evaluated using a calculator that only supports base-10 or base-e. The result is identical regardless of which base you use for the conversion.
What is the difference between log and ln?
log typically denotes log base 10 (common logarithm), while ln denotes the natural logarithm with base e ≈ 2.71828. ln arises naturally in calculus (the integral of 1/x), while log base 10 is convenient for scientific notation and decibel calculations.