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If x is a real number such that 2^(2x+3)=14, find 2^x 

 Jul 13, 2023
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If x is a real number such that 2^(2x+3)=14, find 2^x    

 

In the problem we have 2(2x+ 3) = 14   

 

So:  To what power do we raise 2 in order to produce 14.  

 

The logarithm of a number is the power to which a particular  

base must be raised to produce a specific number.  

 

Example:    23  =  8         so  log2(8) = 3   

                102  =  100     so  log10(100) = 2  

 

The calculator in my iPhone has a button that will calculate logs.   

 

So, log2(14) = 3.8073549 and the decimal fraction keeps going  

but that much of it will get close enough for our purpose.   

 

So 2(3.8073549)  =  14 

 

This exponent is the value needed for the exponent in the problem.  

 

2(2x+3) = 14    therefore  2x + 3  =  3.8073549 

                                       2x        =  0.8073549    

                                         x        =  0.4036775   

 

                                         2x  =  2(0.4036775)   

                                         2x  =  1.32288   

.

 Jul 13, 2023

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