Verified answer

Ответ:

Выразим  n  из равенства .

[tex]R_0\cdot q^{n}=r\cdot \dfrac{q^{n}-1}{q-1}\\\\\\R_0\cdot q^{n}\cdot (q-1)=r\cdot (q^{n}-1)\\\\\\R_0\cdot q^{n}\cdot (q-1)-r\cdot q^{n}=-r\\\\\\q^{n}\cdot \Big(R_0(q-1)-r\Big)=-r\\\\\\q^{n}=\dfrac{-r}{R_0(q-1)-r}\\\\\\q^{n}=\dfrac{-r}{R_0q-R_0-r}\\\\\\q^{n}=\dfrac{r}{r+R_0-R_0q}\\\\\\n=log_{q}\ \dfrac{r}{r+R_0-R_0q}\ \ ,\ \ \ q > 0\ ,\ q\ne 1\ ,\ \ \dfrac{r}{r+R_0-R_0q} > 0[/tex]