2^x - 2^(x-2) = 3* 2^13
(2^(x-2))*2^2 - 2^(x-2) = 3* 2^13
(2^(x-2)) (2^2-1) =3* 2^13
3* (2^(x-2) ) = 3* 2^13
==> x-2 = 13
x=15
Testprep6
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Source: Beat The GMAT — Problem Solving |
2^x - 2^(x-2) = 3* 2^13
HERE 2^x CAN BE WRITTEN AS (2^(x-2+2)) OR (2^(x-2))*(2^2 )
[(2^(x-2))*(2^2)] - [2^(x-2)] = 3* 2^13
NOW AS (2^(x-2)) IS COMMON IN BOTH TERMS, I HAVE IT OUT
[(2^(x-2))] * [(2^2)-1] =3* 2^13
[2^(x-2)] * 3 = 3* 2^13
==> x-2 = 13
X = 15
Hope I am clear now.
HERE 2^x CAN BE WRITTEN AS (2^(x-2+2)) OR (2^(x-2))*(2^2 )
[(2^(x-2))*(2^2)] - [2^(x-2)] = 3* 2^13
NOW AS (2^(x-2)) IS COMMON IN BOTH TERMS, I HAVE IT OUT
[(2^(x-2))] * [(2^2)-1] =3* 2^13
[2^(x-2)] * 3 = 3* 2^13
==> x-2 = 13
X = 15
Hope I am clear now.
2^x - 2^(x-2) = 3* 2^13
HERE 2^x CAN BE WRITTEN AS (2^(x-2+2)) OR (2^(x-2))*(2^2 )
[(2^(x-2))*(2^2)] - [2^(x-2)] = 3* 2^13
NOW AS (2^(x-2)) IS COMMON IN BOTH TERMS, I HAVE IT OUT
[(2^(x-2))] * [(2^2)-1] =3* 2^13
[2^(x-2)] * 3 = 3* 2^13
==> x-2 = 13
X = 15
Hope I am clear now.
HERE 2^x CAN BE WRITTEN AS (2^(x-2+2)) OR (2^(x-2))*(2^2 )
[(2^(x-2))*(2^2)] - [2^(x-2)] = 3* 2^13
NOW AS (2^(x-2)) IS COMMON IN BOTH TERMS, I HAVE IT OUT
[(2^(x-2))] * [(2^2)-1] =3* 2^13
[2^(x-2)] * 3 = 3* 2^13
==> x-2 = 13
X = 15
Hope I am clear now.
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wizardofwashington
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I'm curious why you guys didn't try to use the "plugging in" approach. Given that there are only two answer choices above the value of 13, it didn't take me more than 15 seconds to solve this.
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