document.write( "Question 482777: Log5a+log5b-log5c \n" ); document.write( "

Algebra.Com's Answer #330433 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+log%285%2Ca%29+%2B+log%285%2Cb%29+-+log%285%2Cc%29+\"$
\n" ); document.write( "Make use of 2 rules
\n" ); document.write( "1st rule:
\n" ); document.write( " $\"+log%28a%29+%2B+log%28b%29+=+log%28a%2Ab%29+\"$
\n" ); document.write( "2nd rule:
\n" ); document.write( " $\"+log%28a%29+-+log%28b%29+=+log%28a%2Fb%29+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "Using 1st rule:
\n" ); document.write( " $\"+log%285%2Ca%29+%2B+log%285%2Cb%29+=+log%285%2Ca%2Ab%29+\"$
\n" ); document.write( "Now I have:
\n" ); document.write( " $\"+log%285%2Ca%2Ab%29+-+log%285%2Cc%29+\"$
\n" ); document.write( " $\"+log%285%2C+%28a%2Ab%29%2Fc%29+\"$ answer
\n" ); document.write( "-------------------
\n" ); document.write( "Suppose
\n" ); document.write( " $\"+a+=+5+\"$
\n" ); document.write( " $\"+b+=+25+\"$
\n" ); document.write( " $\"+c+=+625+\"$
\n" ); document.write( " $\"+log%285%2C5%29+%2B+log%285%2C25%29+=+1+%2B+2+\"$
\n" ); document.write( " $\"+1+%2B+2+=+3+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+3+-+log%285%2C625%29+=+3+-+3+=+0+\"$
\n" ); document.write( "compare with:
\n" ); document.write( " $\"+log%285%2C+%28a%2Ab%29%2Fc%29++=+log%285%2C+%285%2A25%29%2F635%29\"$
\n" ); document.write( "which equals
\n" ); document.write( " $\"+log%285%2C1%29+\"$
\n" ); document.write( "The log to the base 5 which equals 1 is 0
\n" ); document.write( "OK \n" ); document.write( "

\n" );