Question

Demonstrați ca log in baza 3 din 7 > log in baza 7 din 3

Answer 1

 

$\displaystyle\bf\\log_3(7)>log_7(3)~~~?...Nu~stim.~Trebuie~sa~calculam.\\\\Rezolvare: \\\\log_3(3)=1~~~si~~~log_3(9)=2\\\\\implies~log_3(7)\in\Big(1,~2\Big)\\\\-----\\\\\sqrt{7}<3~~deoarece~~7<9\\\\log_7(\sqrt{7})=log_7(7^\frac{1}{2})=\frac{1}{2}\\\\log_7(7)=1\\\\\implies~log_7(3)\in\Big(\frac{1}{2},~~1\Big)\\\\\\Orice~numar~din~intervalul:\\\\\Big(1,~2\Big)\\\\este~mai~mare~decat~orice~numar~din~intervalul:\\\\\Big(\frac{1}{2},~~1\Big)\\\\\\ \implies~log_3(7)>log_7(3)$