gmat prep exponents

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Anyone know how to solve this one?

[raunekk]

3^x - 3^x-1 = 162

3^x - 3^x * 3^-1 = 162

taking common


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


3^x * 2/3 = 2 * 3 ^4 (162=2 * 3^4)

3^x-1 * 2 = 3^4 * 2

Comparing the powers on both sides


x-1=4 i.e x=5
thus x(x-1) = 5*4 = 20

[smclean23]

Could you further explain the common factor?