Find n in the equation, 1 - (12/54)^n = 0.95
add $\displaystyle \left(\frac{12}{54}\right)^n$ to both sides
$\displaystyle 1=0.95+\left(\frac{12}{54}\right)^n$
subtract 0.95 from both sides
$\displaystyle 1-0.95=\left(\frac{12}{54}\right)^n$
take logarithms of both sides
$\displaystyle log0.05=log\left(\frac{12}{54}\right)^n$
utilise log laws
$\displaystyle log0.05=n(log12-log54)$
$\displaystyle n=\frac{log0.05}{log12-log54}$