If 2^x - 2^(x-2) = 3(2^17), what is the value of x?
a)16
b)17
c)18
d)19
e)20
Spoiler: I know the answer to this question is d, however in the explanation, they did it algebraically, and I did not understand the factoring.
Explanation:
Factor out 2^(x-2) from the left side of the equation to get:
2^(x-2) * (2^(2)-1) = 3 * 2^17 <----how????
2^(2)-1 = 3, which is equivalent to the 3 on the other side of the equation
x-2 = 17, x = 19
a)16
b)17
c)18
d)19
e)20
Spoiler: I know the answer to this question is d, however in the explanation, they did it algebraically, and I did not understand the factoring.
Explanation:
Factor out 2^(x-2) from the left side of the equation to get:
2^(x-2) * (2^(2)-1) = 3 * 2^17 <----how????
2^(2)-1 = 3, which is equivalent to the 3 on the other side of the equation
x-2 = 17, x = 19
