SOLUTION: how do you evaluate the following expression: log base square root 2 (2 sqaure root 2)

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Question 143557: how do you evaluate the following expression:
log base square root 2 (2 sqaure root 2)
Answer by solver91311(12135) About Me  (Show Source):
You can put this solution on YOUR website!
log%28b%2Cx%29=y means b%5Ey=x and log%28b%2Cxy%29=log%28b%2Cx%29%2Blog%28b%2Cy%29, so

log%28sqrt%282%29%2C2sqrt%282%29%29=log%28sqrt%282%29%2C2%29%2Blog%28sqrt%282%29%2Csqrt%282%29%29

if y=log%28sqrt%282%29%2C2%29, then %28sqrt%282%29%29%5Ey=2. If %28sqrt%282%29%29%5Ey=2 then y=2

if z=log%28sqrt%282%29%2Csqrt%282%29%29, then %28sqrt%282%29%29%5Ez=sqrt%282%29. If %28sqrt%282%29%29%5Ez=sqrt%282%29, then z=1 (In fact, log%28b%2Cb%29+=+1, always)

Therefore: log%28sqrt%282%29%2C2sqrt%282%29%29=log%28sqrt%282%29%2C2%29%2Blog%28sqrt%282%29%2Csqrt%282%29%29=2+%2B+1+=+3