Log Calculator

Logarithms – Quick Cheat Sheet

• Definition: log_b(x) = y ⇔ b^y = x.
• Domain: x > 0, b > 0, b ≠ 1.
• Common bases: log₁₀(x) (common), ln(x) = log_e(x) (natural), log₂(x) (binary).
• Change of base: log_b(x) = ln(x)/ln(b) = log_k(x)/log_k(b).
• Key values: log_b(1)=0; log_b(b)=1.
• Rules: log(xy)=log x + log y; log(x/y)=log x − log y; log(x^k)=k·log x.
• Signs: If 0<x<1 then log_b(x)<0 (for b>1). If x>1 then log_b(x)>0.