Question

1) Log5 1/7-log√5 25/√7
2) 8 в степени log4 3-1

Answer 1

$1); ; log_5, frac{1}{7}-log_{sqrt5}, frac{25}{sqrt7}=log_5, 7^{-1}-(log_{5^{1/2}}, 5^2-log_{5^{1/2}}7^{1/2})=\\\star ; ; log_{a^{k}}, b^{n}=frac{n}{k}, log_{a}, b; ; star \\\=-log_57-frac{2}{1/2}, log_5, 5+log_57=-log_57-4underbrace {log_55}_{1}+log_57=-4$

$2); ; 8^{log_43-1}=(2^3)^{log_{2^2}3-1}=2^{3cdot frac{1}{2}cdot log_2, 3-3}=2^{log_2, 3^{3/2}}cdot 2^{-3}=\\=3^{frac{3}{2}}cdot frac{1}{2^3}=sqrt{3^3}cdot frac{1}{8}=frac{3sqrt3}{8}$

Answer 2

I hope this helps you