Question

216 = (1/36 )^ x−1 how would you solve this?

Answer 1

$216= (\frac{1}{36} )^{x-1} \\ 216=(36^{-1})^{x-1} \\ 216=36^{1-x} \\ 216=36^1*36^{-x} \\ 36^{-x}=216:36 \\ 36^{-x}=6 \\( 6^2)^{-x}=6 \\ 6^{-2x}=6^1 \\ -2x=1 \\ x=- \frac{1}{2}$

Answer 2

$\hbox{convert the numbers to the powers of 6:} \\ 216 = 6^3 \\ \frac{1}{36}=\frac{1}{6^2}=6^{-2} \\ \\ 216=(\frac{1}{36})^{x-1} \\ 6^3=(6^{-2})^{x-1} \\ 6^3=6^{-2(x-1)} \\ 3=-2(x-1) \\ 3=-2x+2 \\ 3-2=-2x \\ 1=-2x \\ x=-\frac{1}{2}$