document.write( "Question 198679: Express as a sum, difference, or multiple of logarithms.\r
\n" ); document.write( "\n" ); document.write( "log(subscript 2)(square root of x / a^2) \n" ); document.write( "

Algebra.Com's Answer #149199 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%282%2C+sqrt%28x%2Fa%5E2%29%29\"$
\n" ); document.write( "The general rule is;
\n" ); document.write( " $\"log%28a%2Fb%29+=+log%28a%29+-+log%28b%29\"$
\n" ); document.write( " $\"log%282%2C%28sqrt%28x%29+%2F+sqrt%28a%5E2%29%29%29\"$
\n" ); document.write( " $\"log%282%2C+x%5E%281%2F2%29%29+-+log%282%2C+%28a%5E2%29%5E+%281%2F2%29%29\"$
\n" ); document.write( "Another general rule is
\n" ); document.write( " $\"log%28a%5Eb%29+=+b%2Alog%28a%29\"$
\n" ); document.write( " $\"%281%2F2%29%2Alog%282%2Cx%29+-+log%282%2Ca%29\"$ answer
\n" ); document.write( "check answer:
\n" ); document.write( "Say $\"x+=+1\"$ and $\"a+=+4\"$
\n" ); document.write( " $\"log%282%2C+sqrt%28x%2Fa%5E2%29%29\"$
\n" ); document.write( " $\"log%282%2C+sqrt%281%2F16%29%29\"$
\n" ); document.write( " $\"log%282%2C+1%2F4%29+=+-2\"$
\n" ); document.write( "and
\n" ); document.write( " $\"%281%2F2%29%2Alog%282%2Cx%29+-+log%282%2Ca%29\"$
\n" ); document.write( " $\"%281%2F2%29%2Alog%282%2C1%29+-+log%282%2C4%29\"$
\n" ); document.write( " $\"%281%2F2%29%2A0+-+2+=+-2\"$
\n" ); document.write( "OK
\n" ); document.write( "Note that $\"log%282%2C-a%29\"$ is impossible. There is no
\n" ); document.write( "log to a positive base that will result in a negative
\n" ); document.write( "number. \n" ); document.write( "

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