Question

Exercitiul 4, va rog
Am încercat și nu reușesc

Answer 1

 

$\displaystyle\bf\\Folosim~formula:\\\\\\log_ab+log_ac=log_a(b\times c)\\\\A=log_3\frac{2}{1}+log_3\frac{3}{2}+log_3\frac{4}{3}+log_3\frac{5}{4}+log_3\frac{6}{5}+log_3\frac{7}{6}+log_3\frac{8}{7}+log_3\frac{9}{8}\\\\A=log_3\left(\frac{2}{1}\times\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\right)$

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$\displaystyle\bf\\A=log_3\left(\frac{2\times3\times4\times5\times6\times7\times8\times9}{1\times2\times3\times4\times5\times6\times7\times8}\right)\\\\Dupa~simplificari~ramanem~cu:\\\\A=log_3(9)\\\\\boxed{\bf~A=2\in N}$