Is 2^x greater than 100?
(1) 2^(sqrt(x)) = 8
(2) 1/2^x < 0.01
[spoiler](1) 2^(sqrt(x)) = 2^3 --> sqrt(x) = 3 --> x = 9 --> 2^9 is greater than 100; SUFFICIENT
(2) 1/2^x < 0.01 --> 2^x > 1/0.01 --> 2^x > 100; SUFFICIENT
ANS: D
I understand the method in (2) but why the sign change? I thought this only happened when you multiply or divide by a negative number or a varible that is negative? Please help explain! And yes I know it is not relevant to answer the question since you only need to know if you can solve for x. This is just for greater understanding of inequalities. Thanks![/spoiler]
(1) 2^(sqrt(x)) = 8
(2) 1/2^x < 0.01
[spoiler](1) 2^(sqrt(x)) = 2^3 --> sqrt(x) = 3 --> x = 9 --> 2^9 is greater than 100; SUFFICIENT
(2) 1/2^x < 0.01 --> 2^x > 1/0.01 --> 2^x > 100; SUFFICIENT
ANS: D
I understand the method in (2) but why the sign change? I thought this only happened when you multiply or divide by a negative number or a varible that is negative? Please help explain! And yes I know it is not relevant to answer the question since you only need to know if you can solve for x. This is just for greater understanding of inequalities. Thanks![/spoiler]
