document.write( "Question 925847: log(5x) = log3+log(x-2) ...Just like that; no bases. PLEASE HELP!! -If you can go step by step with explanations that would be sooo helpful. Thank you!! \n" ); document.write( "
Algebra.Com's Answer #561810 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"log%28%285x%29%29+=+log%28%283%29%29%2Blog%28%28x-2%29%29\"\r\n" );
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document.write( "The base is 10 anytime the base is not written.\r\n" );
document.write( "But actually it doesn't matter what the base is.\r\n" );
document.write( "We just need to know some rules of logaritms\r\n" );
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document.write( "Rule 1:   \"log%28%28A%29%29%2Blog%28%28B%29%29=log%28%28A%2AB%29%29\"\r\n" );
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document.write( "Rule 2:  If \"log%28%28A%29%29=log%28%28B%29%29\" then we can drop the logs and write \"A=B\"\r\n" );
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document.write( "Start with \r\n" );
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document.write( "\"log%28%285x%29%29+=+log%28%283%29%29%2Blog%28%28x-2%29%29\"\r\n" );
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document.write( "We use rule 1 on the right side:\r\n" );
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document.write( "\"log%28%285x%29%29+=+log%28%283%28x-2%29%29%29\"\r\n" );
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document.write( "Now use rule 2\r\n" );
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document.write( "\"5x=3%28x-2%29\"\r\n" );
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document.write( "That's an easy equation to solve.  You should get -3\r\n" );
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document.write( "Trouble is, you must always check your answer to see if it\r\n" );
document.write( "is an actual solution or just an extraneous answer.\r\n" );
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document.write( "\"log%28%285x%29%29+=+log%28%283%29%29%2Blog%28%28x-2%29%29\"\r\n" );
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document.write( "\"log%28%285%28-3%29%29%29+=+log%28%283%29%29%2Blog%28%28-3-2%29%29\"\r\n" );
document.write( "\"log%28%28-15%29%29+=+log%28%283%29%29%2Blog%28%28-5%29%29\"\r\n" );
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document.write( "Oh oh!  -3 is an extraneous answer because there is no such\r\n" );
document.write( "number in real number mathematics as the logarithm of a negative\r\n" );
document.write( "number.  Since when we checked we got a logarithm of a negative\r\n" );
document.write( "number, we knew that the answer we got was extraneous and not a\r\n" );
document.write( "real solution.\r\n" );
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document.write( "THERE IS NO SOLUTION!\r\n" );
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document.write( "Edwin
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