Question

Log2 0,2/log8 50- log8 0,5

Answer 1

$\frac{log_20,2}{log_850-log_80,5}=\frac{log_25^{-1}}{\frac{1}{3}log_2(5^2\cdot 2)-\frac{1}{3}log_22^{-1}}=\frac{-log_25}{\frac{2}{3}log_25+\frac{1}{3}+\frac{1}{3}} =\\\\=- \frac{log_25}{\frac{2}{3}(log_25+1)} =-\frac{3\cdot log_25}{2\cdot (log_25+1)}$