SOLUTION: log square root 100y in expanded form

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Question 383943: log square root 100y in expanded form
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28sqrt%28100y%29%29%29
To start we need to remember that a square root is the same as an exponent of 1/2. So we can rewrite your expression as:
log%28%28%28100y%29%5E%281%2F2%29%29%29
Next we can use a property of logarithms, log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29, to move the exponent of the argument out in front:
%281%2F2%29log%28%28100y%29%29
Next we can use another property of logarithms, log%28a%2C+%28p%2Aq%29%29+=+log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29, to rewrite the log of the product as the sum of the logs of the factors:
%281%2F2%29%28log%28%28100%29%29%2Blog%28%28y%29%29%29
Note the use of parentheses. It is an extremely good habit to use parentheses when substituting. In this case it helps us know that the Distributive Property applies with the 1/2:
%281%2F2%29log%28%28100%29%29%2B%281%2F2%29log%28%28y%29%29
Since the base of log is 10 and since 100+=+10%5E2, log%28%28100%29%29+=+2:
%281%2F2%29%282%29%2B%281%2F2%29log%28%28y%29%29
which simplifies to:
1%2B%281%2F2%29log%28%28y%29%29