SOLUTION: Given Log(a)=0.0441 and log(b)=0.7964; find Log[sqrt a/b] (find log square root of (a) over (b).

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Question 202843: Given Log(a)=0.0441 and log(b)=0.7964; find Log[sqrt a/b] (find log square root of (a) over (b).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28sqrt%28a%29%2Fb%29%29 Start with the given expression.


log%28%28sqrt%28a%29%29%29-log%28%28b%29%29 Break up the log using the identity log%28%28A%2FB%29%29=log%28%28A%29%29-log%28%28B%29%29%29


log%28%28a%5E%281%2F2%29%29%29-log%28%28b%29%29 Convert to exponential notation.


%281%2F2%29log%28%28a%29%29-log%28%28b%29%29 Rewrite the first log using the identity log%28%28x%5Ey%29%29=y%2Alog%28%28x%29%29


%281%2F2%29%280.0441%29-0.7964 Plug in log%28%28a%29%29=0.0441 and log%28%28b%29%29=0.7964


0.02205-0.7964 Multiply


-0.77435 Combine like terms.


So log%28%28sqrt%28a%29%2Fb%29%29=-0.77435 when log%28%28a%29%29=0.0441 and log%28%28b%29%29=0.7964