Question

(Vunesp-SP) Determine n E n a fim de que se tenha:​

Answer 1

Explicação passo-a-passo:

Lembre-se que:

$\sf log_{b}~a+log_{b}~c=log_{b}~(a\cdot c)$

Assim:

$\sf log_{3}~\dfrac{3}{2}+log_{3}~\dfrac{4}{3}+\dots+log~\dfrac{n}{n-1}=2$

$\sf log_{3}~\Big(\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\dots\dfrac{n-1}{n-2}\cdot\dfrac{n}{n-1}\Big)=2$

$\sf log_{3}~\Big(\dfrac{n}{2}\Big)=2$

$\sf \dfrac{n}{2}=3^2$

$\sf \dfrac{n}{2}=9$

$\sf n=2\cdot9$

$\sf \red{n=18}$