document.write( "Question 1102526: log3 (x-4y+5)=0 and log3 (x-1)-log3 y=1\r
\n" ); document.write( "\n" ); document.write( "simaltenously \n" ); document.write( "
Algebra.Com's Answer #717230 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "Learn how to change logarithm equations to and from \r\n" );
document.write( "equivalent exponential equations:\r\n" );
document.write( "\r\n" );
document.write( "\"log%28B%2C%28A%29%29=C\" and \"A=B%5EC\" are equivalent.\r\n" );
document.write( "\r\n" );
document.write( "Therefore your first equation:\r\n" );
document.write( "\r\n" );
document.write( "\"log%283%2C%28x-4y%2B5%29%29=0\" is equivalent to\r\n" );
document.write( "\r\n" );
document.write( "\"x-4y%2B5=3%5E0\" and then\r\n" );
document.write( "\"x-4y%2B5=1\"\r\n" );
document.write( "\"x=4y-4\"\r\n" );
document.write( "\r\n" );
document.write( "Your second equation:\r\n" );
document.write( "\r\n" );
document.write( "\"log%283%2C%28x-1%29%29-log%283%2C%28y%29%29=1\"\r\n" );
document.write( "\r\n" );
document.write( "Using a rule of logarithms, becomes\r\n" );
document.write( "\r\n" );
document.write( "\"log%283%2C%28%28x-1%29y%5E%22%22%29%29=1\", which is equivalent to\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-1%29y=3%5E1\" and then\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-1%29y=3\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting 4y-4 for x:\r\n" );
document.write( "\r\n" );
document.write( "\"%284y-4-1%29y=3\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"y+=+%285+%2B-+sqrt%2825%2B48%29%29%2F8+\"\r\n" );
document.write( "\r\n" );
document.write( "\"y+=+%285+%2B-+sqrt%2873%29%29%2F8+\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting in \"x=4y-4\"\r\n" );
document.write( "\r\n" );
document.write( "\"x=4%28%285+%2B-+sqrt%2873%29%29%2F8%29-4\"\r\n" );
document.write( "\r\n" );
document.write( "\"x=%285+%2B-+sqrt%2873%29%29%2F2-4\"\r\n" );
document.write( "\r\n" );
document.write( "\"x=%285+%2B-+sqrt%2873%29%29%2F2-8%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "\"x=%285-8+%2B-+sqrt%2873%29%29%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "\"x=%28-3+%2B-+sqrt%2873%29%29%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "Since logs cannot be taken of negative numbers, and\r\n" );
document.write( "the original second equation contains \"log%283%2C%28y%29%29\" \r\n" );
document.write( "and \"log%283%2C%28x-1%29%29\", the only solutions are the\r\n" );
document.write( "positive ones:\r\n" );
document.write( "\r\n" );
document.write( "\"x=%28-3+%2B+sqrt%2873%29%29%2F2\" and \"y+=+%285+%2B+sqrt%2873%29%29%2F8+\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );