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How can x be determined if : `log_2(9 - 2^x) = 3 - x`

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rouche | Student, Undergraduate | (Level 1) Honors

Posted January 24, 2012 at 11:56 PM via web

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How can x be determined if : `log_2(9 - 2^x) = 3 - x`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 25, 2012 at 12:02 AM (Answer #1)

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The value of x has to be determined given that : `log_2(9 - 2^x) = 3 - x`.

Using the property of logarithms, `log_2(9 - 2^x) = 3 - x`

=> `9 - 2^x = 2^(3 - x)`

=> `9 - 2^x = 8/2^x`

Let y = 2^x

=> 9 - y = 8/y

=> 9y - y^2 = 8

=> y^2 - 9y + 8 = 0

=> y^2 - 8y - y + 8 = 0

=> y(y - 8) - 1(y - 8) = 0

=> (y - 1)(y - 8) = 0

=> y = 1 and y = 8

As y = 2^x

2^x = 1

=> x = 0

and 2^x = 8

=> x = 3

The values of x are x = 0 and x = 3

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