Question

Помогите решить, в ответе -2, нужно решение.

Answer 1

$\frac{log_{20}100-log_2100}{log_210\cdot log_{20}10}=\frac{log_{20}10^2-log_210^2}{log_210\cdot log_{20}10}=$

$\frac{2log_{20}10-2log_210}{log_210\cdot log_{20}10}=\frac{2log_{20}10}{log_210\cdot log_{20}10}-\frac{2log_210}{log_210\cdot log_{20}10}=$

$\frac{2}{ log_{2}10}-\frac{2}{log_{20}10}=\frac{2}{ \frac{log10}{log2} }-\frac{2}{ \frac{log10}{log20} }=\frac{2}{ \frac{1}{log2} }-\frac{2}{ \frac{1}{log20} }=$

$2log2-2log20=2(log2-log20)=2log \frac{2}{20}= 2log \frac{1}{10}= 2log 10^{-1}=$

$2log 10^{-1}=2\cdot(-1)log10=-2$