Question

ДАЮ 80 БАЛЛОВ
ПРОЛОГАРИФМИРУЙТЕ X ПО ОСНОВАНИЮ 10
СМОТРИТЕ КАРТИНКУ

Answer 1

lg это log по основанию 10
lg(x) = lg((10((100a(0,1aa)^(1/3))^(1/2)))^(1/3))-lg(100*((0,1a)^0,5)) = lg(((10^12)(a^5))^(1/8))-lg((1000a)^(1/2)) = (1/8)lg((10^12)(a^5))-(1/2)lg(1000a) = 1,5lg(a^5)-1,5lg(a) = 7,5lg(a)-1,5lg(a) = 6lg(a)

Answer 2

$\displaystyle\mathtt{x=\frac{\sqrt[3]{10\sqrt{100a\sqrt[3]{0,1a^2}}}}{100\sqrt{0,1a}}}$

1) $\displaystyle\mathtt{\sqrt[3]{0,1a^2}=(10^{-1}a^2)^{\frac{1}{3}}=10^{-\frac{1}{3}}a^{\frac{2}{3}}}$

2) $\displaystyle\mathtt{\sqrt{100a\sqrt[3]{0,1a^2}}=\sqrt{100a*10^{-\frac{1}{3}}a^{\frac{2}{3}}}=(10^{\frac{5}{3}}a^{\frac{5}{3}})^{\frac{1}{2}}=10^{\frac{5}{6}}a^{\frac{5}{6}}}$

3) $\displaystyle\mathtt{\sqrt[3]{10\sqrt{100a\sqrt[3]{0,1a^2}}}=\sqrt[3]{10*10^{\frac{5}{6}}a^{\frac{5}{6}}}=(10^{\frac{11}{6}}a^{\frac{5}{6}})^{\frac{1}{3}}=10^{\frac{11}{18}}a^{\frac{5}{18}}}$

4) $\displaystyle\mathtt{\sqrt{0,1a}=(10^{-1}a)^{\frac{1}{2}}=10^{-\frac{1}{2}}a^{\frac{1}{2}}}$

5) $\displaystyle\mathtt{100\sqrt{0,1a}=100*10^{-\frac{1}{2}}a^{\frac{1}{2}}=10^{\frac{3}{2}}a^{\frac{1}{2}}}$

6) $\mathtt{\frac{\sqrt[3]{10\sqrt{100a\sqrt[3]{0,1a^2}}}}{100\sqrt{0,1a}}=\frac{10^{\frac{11}{18}}a^{\frac{5}{18}}}{10^{\frac{3}{2}}a^{\frac{1}{2}}}=10^{\frac{11}{18}-\frac{3}{2}}a^{\frac{5}{18}-\frac{1}{2}}=10^{-\frac{8}{9}}a^{-\frac{2}{9}}=(10^{4}a)^{-\frac{2}{9}}}$

и наконец, 7) $\mathtt{\lg x=\lg\frac{\sqrt[3]{10\sqrt{100a\sqrt[3]{0,1a^2}}}}{100\sqrt{0,1a}}=\lg(10^{4}a)^{-\frac{2}{9}}=-\frac{2}{9}\lg a-\frac{8}{9}}$