Problem Solving

if 3 ^x - 3^x-1=162 then x(x-1) =

if 3 ^x - 3^x-1=162 then x(x-1) =

3^5 - 3^4 = 162
Thus x = 5
5(5-1) = 5.4=20

3^x - 3^x-1 = 162

3^x(1-3^-1) = 162

3^x(1-1/3) = 162 ==> 3^x* 2/3 = 162

3^x/3 = 81

3^(x-1) = 3^4

(x-1) = 4

x = 5 ===> x(x-1) = 5 * 4 = 20

thanks sudhirsk, quick question though. if 3^x*2/3=162 why then wasnt 162(3/2) why did you divide 162 by 2 instead of multiplying it by 3/2. Please explain to better my understanding. It looks like I might have gone wrong right there. so for future if the base is equal to the denominator then divide by the numerator?