Question

Найди z, если lgz=lg(k2−u2)−2lg(k+u).

Answer 1

$lgz=lg(k^2-u^2)-2lg(k+u)\\\\lgz=lg(k^2-u^2)-lg(k+u)^2\\\\lgz=lg\frac{k^2-u^2}{(k+u)^2}\\\\lgz=lg\frac{(k+u)(k-u)}{(k+u)^2}\\\\lgz=lg\frac{k-u}{k+u}\\\\z=\frac{k-u}{k+u}$