Выражение с логарифмами.

[latex]a= log_{36} 108[/latex]       [latex]log_{2} 3 -[/latex] ? [latex] log_{36} 108= log_{36} (36*3)= log_{36} 36+ log_{36} 3=1+ log_{6^2}3=1+ \frac{1}{2} log_{6} 3=[/latex][latex]1+ \frac{1}{2} * \frac{log_{2} 3}{log_{2} 6}=1+ \frac{1}{2}* \frac{log_{2} 3}{log_{2} 2+{log_{2} 3}}=1+ \frac{1}{2}* \frac{log_{2} 3}{1+{log_{2} 3}}[/latex] [latex]1+ \frac{1}{2}* \frac{log_{2} 3}{1+{log_{2} 3}}=a[/latex] [latex] \frac{1}{2}* \frac{log_{2} 3}{1+{log_{2} 3}}=a-1[/latex] [latex] \frac{log_{2} 3}{1+{log_{2} 3}}=2(a-1)[/latex] [latex]log_{2} 3}=2(a-1)*(1+{log_{2} 3})[/latex] [latex]log_{2} 3}-2{log_{2} 3}*(a-1)=2(a-1)[/latex] [latex]log_{2} 3}*(1-2(a-1))=2(a-1)[/latex] [latex]log_{2} 3}*(1-2a+2)=2(a-1)[/latex] [latex]log_{2} 3}*(3-2a)=2(a-1)[/latex] [latex]log_{2} 3}= \frac{2(a-1)}{3-2a} [/latex] [latex]log_{2} 3}= \frac{2(1-a)}{2a-3} [/latex] Ответ: С) [latex]log_{2} 3}= \frac{2(1-a)}{2a-3} [/latex]