Question

Log2(5-√3)+(5+√3)-log2^11

Answer 1

Ne folosim de urmatoarele reguli
$\log_{c}{a}+\log_{c}{b}=\log_{c}{(a*b)}$
$\log_{c}{a}-\log_{c}{b}=\log_{c}{\frac{a}{b}}$
$(a-b)(a+b)=a^{2}-b^{2}$
Atunci
$\log_{2}{5-\sqrt{3}}+\log_{2}{5-\sqrt{3}}-\log_{2}{11}=\log_{2}{(5-\sqrt{3})(5+\sqrt{3})}-\log_{2}{11}=\log_{2}{(25-3)}-\log_{2}{11}=\log_{2}{\frac{22}{11}}=\log_{2}{2}=1$