Question

Помогите эти две номера решить срочно до субботы.

Answer 1

$\displaystyle 3 log_{\frac{a^3}{b}}(\frac{\sqrt{a}}{\sqrt[3]{b}})+log_{\frac{a^3}{b}}(b)=log_{\frac{a^3}{b}}(\frac{\sqrt{a}^3}{\sqrt[3]{b}^3}*b)=log_{\frac{a^3}{b}}(a^{\frac{3}{2}})=\\\\=\frac{1}{log_{a^{\frac{3}{2}}}(\frac{a^3}{b})}=\frac{3}{2(log_aa^3-log_ab)}=\frac{3}{2(3-2)}=\frac{3}{2}$

$\displaystyle log_{\frac{\sqrt{b}}{a^2}}(\frac{\sqrt{a}}{\sqrt[4]{b}})+log_{\frac{\sqrt{b}}{a^2}}(b\sqrt{a} )^{\frac{1}{4}}=log_{\frac{\sqrt{b}}{a^2}}(\frac{a^{\frac{1}{2}}}{b^{\frac{1}{4}}}*b^{\frac{1}{4}}*a^{\frac{1}{8})}=log_{\frac{\sqrt{b}}{a^2}}(a^{\frac{5}{8}})=\\\\=\frac{5}{8}*\frac{1}{log_a(\frac{\sqrt{b}}{a^2})}=\frac{5}{8}*\frac{1}{log_a\sqrt{b}-log_aa^2}=\frac{5}{8}*\frac{1}{\frac{1}{2}*14-2}=\frac{5}{8}*\frac{1}{5}=\frac{1}{8}$