SOLUTION: how to change this to base 4? log64 512

Question 270229: how to change this to base 4?
log64 512
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
how to change this to base 4?
log64 512
log64 512 = x (set it equal to x)
base b = 64
set y = 512
b^x = y --> 64^x = 512 --> 64 * 64^(1/2) = 512 --> x=3/2
logb (x) = logd (x) / logd (b) (d here is your new base)
4^0 = 1, 4^1 = 4, 4*4 = 16, 16*4 = 64, 64*4 = 256 , 256*2 = 512, 256 * 4 = 1024
log64 (512) = log4 (512) / log4 (64)
512/64 = 4^(4.5)/4^3 = 4*4*4*4*4^(1/2) / 4*4*4 = 4*4^(1/2) = 4^(3/2) = 8
log64 (512) = log4 (8) = 3/2
or 64^(3/2) = 512 and 4^(3/2) = 8

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