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

 Dec 23, 2018
 #1
avatar+101798 
+1

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

 

2^(2x + 3)  = 14         

 

2^(2x) * 2^3  = 14

 

2^(2x) * 8  =  14       divide both sides by 8

 

2^(2x)  =  14/8

 

2^(2x) =  7/4       and we can write

 

(2^x)^2 =  7/4        since an exponential can never be nrgative,   take the positive root

 

2^x  =  √7 / 2

 

 

cool cool cool

 Dec 23, 2018
 #2
avatar+701 
+1

CPHill, I have a question about logarithms and functions too. 

 

Let \(f(n) = \){ \(n^2 + 1\)     if n is odd.

                   {  \(\dfrac{n}{2}\)    if n is even.

For how many integers n from 1 to 100, inclusive, does \(f(f(...f(n)...)) = 1\) for some number of applications of f?

 

Thanks!

PartialMathematician  Dec 23, 2018
edited by PartialMathematician  Dec 23, 2018

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