document.write( "Question 1145291: Given that log6 base 3=m and log 5 base 6=n. Express log 10 base 3 in terms of m and n \n" ); document.write( "
Algebra.Com's Answer #766506 by ikleyn(52832)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "Since 10 = 2*5, you have \r\n" );
document.write( "\r\n" );
document.write( "\"log%283%2C+%2810%29%29\" = \"log%283%2C+%282%2A5%29%29\" = \"log%283%2C+%282%29%29\" + \"log%283%2C+%285%29%29\".    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"log%283%2C+%285%29%29\" is given to you as the value  n = \"log%283%2C+%285%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Your task is to retrieve  \"log%283%2C+%282%29%29\"  from the given data.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is simple:  m = \"log%283%2C+%286%29%29\" = \"log%283%2C+%282%2A3%29%29\" = \"log%283%2C+%282%29%29\" + \"log%283%2C+%283%29%29\" = \"log%283%2C+%282%29%29\" + 1;\r\n" );
document.write( "\r\n" );
document.write( "hence,  \"log%283%2C+%282%29%29\" = m-1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, from the formula (1)  \"log%283%2C+%2810%29%29\" = (m-1) + n = m + n - 1.    ANSWER\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Edwin,  thanks for noticing my error !\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I was in hurry and mistakenly read  \"log 5 base 6\"  as   \"log%283%2C%285%29%29\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );