Wiedząc, że [latex] log_{3} 20=a [/latex] i  [latex] log_{3} 15=b [/latex] oblicz [latex]log_{2} 360[/latex] Krok po kroku, Z góry dzięki

Witaj. [latex]log_{3}20=a\\log_{3}15=b ightarrow log_{3}3+log_{3}5=b ightarrow log_{3}5=b-1\\log_{2}360=frac{log_{3}360}{log_{3}2}=frac{log_{3}(9cdot5cdot8)}{log_{3}sqrt{frac{20}{5}}}=frac{log_{3}9+log_{3}5+log_{3}8}{log_{3}(frac{20}{5})^{frac{1}{2}}}=\\=frac{log_{3}3^{2}+log_{3}5+log_{3}2^{3}}{frac{1}{2}(log_{3}20-lo_{3}5)}=frac{2+log_{3}5+3cdot(frac{1}{2}(log_{3}20-log_{3}5))}{frac{1}{2}(log_{3}20-log_{3}5)}=[/latex] [latex]=frac{2+b-1+frac{3}{2}cdot(a-b+1)}{frac{1}{2}cdot(a-b+1)}=frac{2+b-1+1,5a-1,5b+1,5}{0,5a-0,5b+0,5}=frac{1,5a-0,5b+2,5}{0,5a-0,5b+0,5}=frac{3a-b+5}{a-b+1}[/latex]