Problem Solving

whats the easy way to do this problem?

Ok you want to get the left side to have the same exponents first.

2^x = (2^2)(2^x-2) : when we multiply items with exponents we are adding the exponents, so 2+x-2 is the same thing as x.

next think of the 2^2 as a 4. (4)(2^x-2)-(2^x-2) is equal to 3(2^x-2)

we now have 3(2^x-2)=3(2^13)

cancel out the threes you get 2^x-2 = 2^13
now just compare the exponents: x-2 = 13
x=15

2^X- 2^(X-2)= 2^X- 2^X/4
so options 1 ,2 and 3 are out because x must be >13

check for the other two options

2^15- 2^15/4= 2^15-2^13=2^15(4-1)=3*2^13
answer D

2^x - 2^(x-2) = 2^x(1 - 1/4) = 2^x(3/4)
= 2^(x-2)3 = 2^13.3
=>x-2 = 13 => x = 15

2^x(1-1/4)=3(2^13)
2^x(3/4)=3(2^13)
2^x= (4/3)*3(2^13)
2^x=2^2*2^13
x=15