document.write( "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). \n" ); document.write( "

Algebra.Com's Answer #153007 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%28%28sqrt%28a%29%2Fb%29%29\"$ Start with the given expression.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"log%28%28sqrt%28a%29%29%29-log%28%28b%29%29\"$ Break up the log using the identity $\"log%28%28A%2FB%29%29=log%28%28A%29%29-log%28%28B%29%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"log%28%28a%5E%281%2F2%29%29%29-log%28%28b%29%29\"$ Convert to exponential notation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%281%2F2%29log%28%28a%29%29-log%28%28b%29%29\"$ Rewrite the first log using the identity $\"log%28%28x%5Ey%29%29=y%2Alog%28%28x%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%281%2F2%29%280.0441%29-0.7964\"$ Plug in $\"log%28%28a%29%29=0.0441\"$ and $\"log%28%28b%29%29=0.7964\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"0.02205-0.7964\"$ Multiply\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-0.77435\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"log%28%28sqrt%28a%29%2Fb%29%29=-0.77435\"$ when $\"log%28%28a%29%29=0.0441\"$ and $\"log%28%28b%29%29=0.7964\"$ \n" ); document.write( "

\n" );