Question

Вычислите логарифм $log_{ sqrt{2}+ sqrt{1} }( sqrt{2} - sqrt{1})$

Answer 1

$sqrt1=1; ; to$ 
  $sqrt2-1=frac{(sqrt2-1)(sqrt2+1)}{sqrt2+1}=frac{2-1}{sqrt2+1}=frac{1}{sqrt2+1}\\log_{sqrt2+1}{(sqrt2-1)}=log_{sqrt2+1}frac{1}{sqrt2+1}=\\=log_{sqrt2+1}{(sqrt2+1)^{-1}}=-log_{sqrt2+1}{(sqrt2+1)}=-1$