# Math Help - How to get the exponent!!!

1. ## How to get the exponent!!!

Find n in the equation, 1 - (12/54)^n = 0.95

2. Originally Posted by littlesohi
Find n in the equation, 1 - (12/54)^n = 0.95
add $\left(\frac{12}{54}\right)^n$ to both sides

$1=0.95+\left(\frac{12}{54}\right)^n$

subtract 0.95 from both sides

$1-0.95=\left(\frac{12}{54}\right)^n$

take logarithms of both sides

$log0.05=log\left(\frac{12}{54}\right)^n$

utilise log laws

$log0.05=n(log12-log54)$

$n=\frac{log0.05}{log12-log54}$