document.write( "Question 461940: How do you solve a problem that has a divided variable as a base of a logarithm?
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Algebra.Com's Answer #316714 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
\"log%28a%2C%28x%29%29%2Flog%28a%2Fb%2C%28x%29%29\"
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document.write( "Using the change of base formula on the numerator only to\r\n" );
document.write( "natural logs:\r\n" );
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document.write( "\"NUMERATOR+=log%28a%2C%28x%29%29=ln%28x%29%2Fln%28a%29\"\r\n" );
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document.write( "Using the change of base formula on the denominator only to\r\n" );
document.write( "natural logs: [Note: you could use logs base 10 if you prefer]\r\n" );
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document.write( "\"DENOMINATOR+=+log%28a%2Fb%2C%28x%29%29=ln%28x%29%2Fln%28a%2Fb%29\"\r\n" );
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document.write( "So we have\r\n" );
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document.write( "\"log%28a%2C%28x%29%29%2Flog%28a%2Fb%2C%28x%29%29\"\"%22%22=%22%22\"\"NUMERATOR\"\"%22%F7%22\"\"DENOMINATOR\"\"%22%22=%22%22\"\"ln%28x%29%2Fln%28a%29\"\"%22%F7%22\"\"ln%28x%29%2Fln%28a%2Fb%29\"\"%22%22=%22%22\"\"ln%28x%29%2Fln%28a%29\"\"%22%22%2A%22%22\"\"ln%28a%2Fb%29%2Fln%28x%29\"\"%22%22=%22%22\"\"cross%28ln%28x%29%29%2Fln%28a%29\"\"%22%22%2A%22%22\"\"ln%28a%2Fb%29%2Fcross%28ln%28x%29%29\"\"%22%22=%22%22\"\"ln%28a%2Fb%29%2Fln%28a%29\"\"%22%22=%22%22\"\"%28ln%28a%29+-+ln%28b%29%29%2Fln%28a%29\"\"%22%22=%22%22\"\"ln%28a%29%2Fln%28a%29-ln%28b%29%2Fln%28a%29+=+1-ln%28b%29%2Fln%28a%29\"\r\n" );
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document.write( "If you prefer to use logs base 10 then just replace \r\n" );
document.write( "all the \"%22ln%28_%29%22\"'s with \"%22log%28_%29%22\"'s and the answer will be\r\n" );
document.write( "\"1-%22log%28b%29%22%2F%22log%28a%29%22\".\r\n" );
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document.write( "Edwin
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