document.write( "Question 205650: Assume x>0 and 3x-1>0. Rewrite the following expression as a single logarithm. \r
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Algebra.Com's Answer #155276 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Assume x>0 and 3x-1>0. Rewrite the following expression as a single logarithm.
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document.write( "\"2ln%28x%29-%281%2F2%29ln%289x%5E2-1%29%2B+%281%2F2%29ln+%283x%2B1%29+\"\r\n" );
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document.write( "Use the fact that \"A%2Aln%28B%29+=+ln%28A%5EB%29\" on each of the\r\n" );
document.write( "three terms:\r\n" );
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document.write( "\"+ln%28x%5E2%29-ln%289x%5E2-1%29%5E%281%2F2%29%2B+ln+%283x%2B1%29%5E%281%2F2%29\"\r\n" );
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document.write( "Use the fact that \"ln%28A%29-ln%28B%29=ln%28A%2FB%29\" on the first\r\n" );
document.write( "two terms:\r\n" );
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document.write( "\"+ln%28%28x%5E2%29%2F%289x%5E2-1%29%5E%281%2F2%29%29%2B+ln+%283x%2B1%29%5E%281%2F2%29\"\r\n" );
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document.write( "Use the fact that \"ln%28A%29%2Bln%28B%29=ln%28A%2AB%29\" \r\n" );
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document.write( "\"+ln%28%28x%5E2%2F%289x%5E2-1%29%5E%281%2F2%29%29%283x%2B1%29%5E%281%2F2%29%29\"\r\n" );
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document.write( "You actually have it as a single logarithm at this step.\r\n" );
document.write( "However, your teacher probably wants you to simplify it.  \r\n" );
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document.write( "Put the second factor over 1 so you will have two\r\n" );
document.write( "fractions to multiply:\r\n" );
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document.write( "Indicate the multiplication of tops and bottoms of \r\n" );
document.write( "those fractions:\r\n" );
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document.write( "\"+ln%28++%28x%5E2%283x%2B1%29%5E%281%2F2%29%29++%2F%28%289x%5E2-1%29%5E%281%2F2%29%29%29\"\r\n" );
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document.write( "Factor \"9x%5E2-1\" as \"%283x-1%29%283x%2B1%29\"\r\n" );
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document.write( "Use the fact that \"%28A%2AB%29%5EN=A%5EN%2AB%5EN\" to rewrite the\r\n" );
document.write( "denominator:\r\n" );
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document.write( "Cancel:\r\n" );
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document.write( "\"+ln%28++x%5E2++%2F%28%283x-1%29%5E%281%2F2%29%29%29\"\r\n" );
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document.write( "Change the \"1%2F2\" power to a square root:\r\n" );
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document.write( "\"+ln%28++x%5E2++%2Fsqrt%283x-1%29%29\"\r\n" );
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document.write( "Edwin
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