document.write( "Question 383943: log square root 100y in expanded form \n" ); document.write( "

Algebra.Com's Answer #271854 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%28%28sqrt%28100y%29%29%29\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"log%28%28%28100y%29%5E%281%2F2%29%29%29\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"%281%2F2%29log%28%28100y%29%29\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"%281%2F2%29%28log%28%28100%29%29%2Blog%28%28y%29%29%29\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"%281%2F2%29log%28%28100%29%29%2B%281%2F2%29log%28%28y%29%29\"$
\n" ); document.write( "Since the base of log is 10 and since $\"100+=+10%5E2\"$ , $\"log%28%28100%29%29+=+2\"$ :
\n" ); document.write( " $\"%281%2F2%29%282%29%2B%281%2F2%29log%28%28y%29%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"1%2B%281%2F2%29log%28%28y%29%29\"$
\n" ); document.write( " \n" ); document.write( "

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