document.write( "Question 6587: I can't figure out the solution to this equation, or if a real solution really exists. $\"+log%284%2C+w%29+%2B+log%284%2C+6%29+=+log%284%2C+24%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #3579 by Mike(39) $\"\"$ $\"About$

You can put this solution on YOUR website!
There are three laws of logs which you HAVE to now. In order to solve this problem, you need to know that when you add logs with the same base, you multiply the values and transform it into one log. What I mean by that is the following:\r
\n" ); document.write( "\n" ); document.write( "1) $\"+log%284%2C+w%29+%2B+log%284%2C+6%29+=+log%284%2C+24%29+\"$
\n" ); document.write( "2) $\"+log%284%2C+6w%29+=+log%284%2C+24%29\"$ - in this step I have combined the two logs, because the addition of logs allows you to multiply their values (in this case, w * 6.
\n" ); document.write( "3) 6w = 24 - you can cancel the logs because they have the same base and one of them has a variable in it.
\n" ); document.write( "4) w = 4\r
\n" ); document.write( "\n" ); document.write( "Hope that helps.
\n" ); document.write( "Regards,
\n" ); document.write( "-Mike \n" ); document.write( "

\n" );