factoring out 3^(x-1) you get
3^(x-1) * (3^1 - 1) or 3^(x-1) *2 = 162
therefor 3^(x-1) = 81
but 3^4 = 81 so x = 5.
x*(x-1) = 5*4 = 20

I suspect you copied the second one incorrectly and are asking about
2^x - 2^(x-2) = 3(2^13)

IN that case you get 2^(x-2) * (2^2 - 1) = 2^(x-2) * (4-1) = 3 * 2^(x-2)
therefore x-2 = 13 and x = 15

wow, awesome, thanks for the quick reply. I just stumbled onto this forum and it is amazing.

Glad to help!