Логарифмы

log_ab = c

a^c = b

a^log_ab = b

log_a1 = 0

log_aa = 1

lga = log₁₀a

lna = log_ea

1) log_axy = log_ax + log_ay

2) ${\text{log}}_a\frac{x}{y}={\text{log}}_{a}x-{\text{log}}_{a}y$

3) log_axⁿ = n log_ax

4) log_aⁿx = $\frac{1}{n}$ log_ax

5) ${\text{log}}_{a^n}{x}^m=\frac{m}{n}{\text{log}}_{a}x$

6) ${\text{log}}_{a}b=\frac{{\text{log}}_{c}b}{{\text{log}}_{c}a}$

7) ${\text{log}}_{a}b=\frac{1}{{\text{log}}_{b}a}$

8) a^log_cb = b^log_ca