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If f(4) = 1 and f(2x) = 3f(x) for all x, then find f(64).

 Feb 17, 2022
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Since we know that f(4) = 1, we can plug that information into the second equation and get:

 

f(2*4) = 3f(4)

f(8) = 3*1

f(8) = 3

 

f(2*8) = 3f(8)

f(16) = 3*3

f(16) = 9

 

f(2*16) = 3f(16)

f(32) = 3*9

f(32) = 27

 

f(2*32) = 3f(32)

f(64) = 3*27

f(64) = 81

 

Hope this helped. Let me know if I did anything wrong!

 Feb 17, 2022

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