Question

кто шарит в логарифмах помогите,если не трудно

Answer 1

$\mathtt{\sqrt{5}^{~\log_5(\sqrt{2}-1)^2}+\sqrt{3}^{~\log_3(\sqrt{2}-2)^2}=(5^{\frac{1}{2}})^{\log_5(\sqrt{2}-1)^2}+(3^{\frac{1}{2}})^{\log_3(\sqrt{2}-2)^2}=}\\\mathtt{5^{\frac{\log_5(\sqrt{2}-1)^2}{2}}+3^{\frac{\log_3(\sqrt{2}-2)^2}{2}}=5^{\frac{2\log_5|\sqrt{2}-1|}{2}}+3^{\frac{2\log_3|\sqrt{2}-2|}{2}}=}\\\mathtt{5^{\log_5|\sqrt{2}-1|}+3^{\log_3|\sqrt{2}-2|}=|\sqrt{2}-1|+|\sqrt{2}-2|=\sqrt{2}-1+2-\sqrt{2}=1}$