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What are all the values of x for which log base2 (9-2^x)=3-x?

 May 1, 2019
 #1
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log 2 (9-2^x) = 3-x   ......in exponential form, we have

 

2^(3-x)  = 9 - 2^x

 

2^(3 - x) +  2^x  =  9

 

2^3 / 2^x  + 2^x = 9

 

2^3 + 2^(2x) = 9^(x)

 

2^(2x) - 9^(x) + 8  = 0

 

(2^x  - 8) ( 2^x - 1)  = 0

 

 

So    we have that either 

 

2^x - 8  = 0             or          2^x  - 1  = 0

2^x  =  8                              2^x  = 1

x = 3                                       x = 0

 

 

 

cool cool cool

 May 1, 2019

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