Выразите lg A через логарифмы простых чисел

Решите задачу:

$5)\; \; A= \frac{ \sqrt[3]{2}\cdot \sqrt[4]{8} }{\sqrt{12}} = \frac{2^{\frac{1}{3}}\cdot 2^{\frac{3}{4}}}{(2^2\cdot 3)^{\frac{1}{2}}} = \frac{2^{\frac{13}{12}}}{2\cdot 3^{\frac{1}{2}}} =2^{\frac{1}{12}}\cdot 3^{-\frac{1}{2}}\\\\lgA=lg(2^{\frac{1}{12}}\cdot 3^{-\frac{1}{2}})=lg2^{\frac{1}{12}}+lg3^{-\frac{1}{2}}=\frac{1}{12}\cdot lg2-\frac{1}{2}lg3$

$6)\; \; A= \frac{21^{\frac{3}{4}}\cdot \sqrt[3]{147}}{\sqrt5} =\frac{(3\cdot 7)^{\frac{3}{4}}\cdot (3\cdot 7^2)^{\frac{1}{3}}}{5^{\frac{1}{2}}}= \frac{3^{\frac{3}{4}+\frac{1}{3}}\cdot 7^{\frac{3}{4}+\frac{2}{3}}}{5^{\frac{1}{2}}} =3^{\frac{13}{12}}\cdot 7^{\frac{17}{12}}\cdot 5^{-\frac{1}{2}}\\\\lgA= \frac{13}{12}lg3+\frac{17}{12}lg7 -\frac{1}{2} lg5$

$7)\; \; A= \sqrt{\frac{7\sqrt2}{3\sqrt5}} =\Big ( \frac{7\cdot 2^{\frac{1}{2}}}{3\cdot 5^{\frac{1}{2}}} \Big )^{\frac{1}{2}}=7^{\frac{1}{2}}\cdot 2^{\frac{1}{4}}\cdot 3^{-\frac{1}{2}}\cdot 5^{-\frac{1}{4}}$

$lgA= \frac{1}{2}\, lg7+ \frac{1}{4}\, lg2 -\frac{1}{2}\, lg3 -\frac{1}{4}\, lg5\\\\8)\; \; A=8\sqrt[7]{3^4\cdot 5^{\frac{2}{3}}} =2^3\cdot 3^{\frac{4}{7}}\cdot 5^{\frac{2}{21}}\\\\lgA=3\, lg2+\frac{4}{7}\, lg3+\frac{2}{21}\, lg5$