document.write( "Question 122347: log base 3 of (x+2)-log base 3 of (x-3)= log base 3 of 6 ; slove for x.\r
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Algebra.Com's Answer #89843 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Your equation is:  \"log%283%2C%28x%2B2%29%29-log%283%2C%28x-3%29%29=log%283%2C6%29\"\r\n" );
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document.write( "First apply the difference of logs rule:\r\n" );
document.write( "\"log%28b%2Ca%29-log%28b%2Cc%29=log%28b%2C%28a%2Fc%29%29\"\r\n" );
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document.write( "\"log%283%2C%28x%2B2%29%29-log%283%2C%28x-3%29%29=log%283%2C6%29\"\r\n" );
document.write( "\"log%283%2C%28%28x%2B2%29%2F%28x-3%29%29%29=log%283%2C6%29\"\r\n" );
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document.write( "Now, if \"log%28b%2Ca%29=log%28b%2Cc%29\" then \"a=c\", so\r\n" );
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document.write( "\"log%283%2C%28%28x%2B2%29%2F%28x-3%29%29%29=log%283%2C6%29\" => \"%28x%2B2%29%2F%28x-3%29=6\"\r\n" );
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document.write( "\"%28x%2B2%29%2F%28x-3%29=6\"\r\n" );
document.write( "\"x%2B2=6%28x-3%29\"\r\n" );
document.write( "\"x%2B2=6x-18\"\r\n" );
document.write( "\"x-6x=-18-2\"\r\n" );
document.write( "\"-5x=-20\"\r\n" );
document.write( "\"x=4\"\r\n" );
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\r\n" ); document.write( "Check the answer\r\n" ); document.write( "\"log%283%2C%28x%2B2%29%29-log%283%2C%28x-3%29%29=log%283%2C6%29\"\r\n" ); document.write( "\"log%283%2C%284%2B2%29%29-log%283%2C%284-3%29%29=log%283%2C6%29\"\r\n" ); document.write( "\"log%283%2C6%29-log%283%2C1%29=log%283%2C6%29\"\r\n" ); document.write( "\r\n" ); document.write( "But \"log%28b%2C1%29=0\", so\r\n" ); document.write( "\"log%283%2C6%29=log%283%2C6%29\", Answer checks.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "
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