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1. if 3 = k * 2^r and 15 = k*4^r then what is r

 Aug 7, 2020
edited by Leaded  Aug 7, 2020
 #1
avatar+26635 
+1

3 = k 2^r       and 15 = k 2^2r

Multiply first equation by 5    and equate the two equations

     NOTE:   k 4^2  =  k  (2^2)^r   =  k 22r

5 k 2^r  = k 2^2r     divide out k

 

5 * 2^r = 2^2r             take log of both sides

 

log 5 + r log 2   = 2r log 2

log 5 = r (2log2 - log2)

 

log5 / log 2 = r   = 2.321928095             (and k = 3/5)

 Aug 7, 2020
edited by ElectricPavlov  Aug 7, 2020
edited by ElectricPavlov  Aug 7, 2020
edited by ElectricPavlov  Aug 7, 2020
 #2
avatar+117 
0

its not k * 2^2r its k*2^r

Leaded  Aug 7, 2020
 #3
avatar+26635 
+1

Guess I did too many steps in my head and lost ya

 

15 = k 4^r =  k * (2^2)^r    =   k *  2^2r

ElectricPavlov  Aug 7, 2020

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