The question is...
Rewrite the equation tn=ar^n-1 to solve for 'n'
$\displaystyle t_n = ar^{n - 1}$
$\displaystyle \Rightarrow r^{n - 1} = \frac {t_n}{a}$
$\displaystyle \Rightarrow ln \left( r^{n - 1} \right) = ln \left( \frac {t_n}{a} \right) $
$\displaystyle \Rightarrow (n - 1) ln(r) = ln \left( \frac {t_n}{a} \right) $
$\displaystyle \Rightarrow n = \frac {ln \left( \frac {t_n}{a} \right) }{ln(r)} + 1$