Question

Ради Хреста Спасителя ПОМОГИТЕ, УМОЛЯЮ, УМНЫЕ МАТЕМАТИКИ!!! ​

Answer 1

$\displaystyle\bf\\\frac{log_{2} 800}{log_{800}2 } -\frac{log_{2} 625}{log_{160} 2} =\frac{log_{2}800 }{\frac{1}{log_{2} 800} } -\frac{log_{2} 625}{\frac{1}{log_{2} 160} } =log^{2}_{2} 800-log_{2} 625\cdot log _{2} 160=\\\\\\=(log_{2} (25\cdot 32))^{2} -log_{2} 5^{4} \cdot log_{2} (5\cdot 32)=\\\\=[log_{2} (5^{2}\cdot2^{5} ]^{2} -4log_{2} 5\cdot(log_{2} 5 +log_{2} 2^{5} )=$

$\displaystyle\bf\\=(log_{2} 5^{2} +log_{2} 2^{5} )^{2} -4log_{2}5\cdot (log_{2} 5+5) =\\\\=(2log_{2}5+5)^{2} -4log^{2} _{2} 5-20log_{2} 5=\\\\=4log^{2} _{2} 5+20log_{2} 5+25-4log^{2} _{2} 5-20log_{2} 5=25$