Библиотека

${\text{log}}_{a}1\text{=0}$

${\text{log}}_{a}a\text{=1}$

${\text{log}}_a\text{bc}={\text{log}}_{a}b+{\text{log}}_{a}c$

${\text{log}}_a\left(\frac{b}{c}\right)={\text{log}}_{a}b-{\text{log}}_{a}c$

${\text{log}}_a{b}^n\text{=n}\cdot {\text{log}}_{a}b$

${\text{log}}_{a^k}b=\frac{1}{k}\cdot {\text{log}}_{a}b$

${\text{log}}_{a^k}{b}^n=\frac{n}{k}\cdot {\text{log}}_{a}b$

logₐⁿ bⁿ = logₐ b

a > 0

a ≠ 1

b > 0

c > 0

d > 0

d ≠ 1

${\text{log}}_{a}b=\frac{{\text{log}}_{d}b}{{\text{log}}_{d}a}=\frac{1}{{\text{log}}_{b}a}$ ──────▶

${\text{log}}_{a}b\cdot {\text{log}}_{b}a\text{=1}$

aˡᵒᵍᵦᶜ = cˡᵒᵍᵦᵃ

Переход к новому основанию логарифма