Question

Помогите с логарифмами, не шарююю!! На своём листочке подробно, Номера 4,5,6; 25 баллов

Answer 1

$( \sqrt[3]{5})^{3+log5(27)}=( \sqrt[3]{5})^3*( \sqrt[3]{5})^{log5(27)} = \\ 5*5^{log5(27^ \frac{1}{3}) }= =5*27^ \frac{1}{3}=5*(3^3)^ \frac{1}{3}=15$
$(log10(25)-log10(0,25))^{-3} = \frac{1}{(lg(25)-lg(0,25))^{-3} } = \frac{1}{lg^3(25:0,25)}= \\ = \frac{1}{lg^3(100)}= \frac{1}{2^3}=0,125 \\ lg(100)=lg(10^2)=2$
$\frac{log_{7} (8)}{log_{ \frac{1}{49} }( \sqrt{2} ) } = \frac{ \frac{log7(8)}{log7( \sqrt{2)} } }{log7( \frac{1}{49}) } =log7(8)* \frac{log7( \frac{1}{49} )}{log7( \sqrt{2} )} = \frac{log7(8)log7( \frac{1}{49}) }{log7( \sqrt{2} )} = \frac{log7(8)(-2)}{log7( \sqrt{2}) } = \\ \\ \\ = \frac{3log7(2)(-2)}{ \frac{1}{2}log7(2) }= \frac{3(-2)}{ \frac{1}{2} }=-12$