document.write( "Question 304781: Express \"e%5E%28log%284%2Cx%29%29\" as a power of x.\r
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Algebra.Com's Answer #218279 by Edwin McCravy(20065)\"\" \"About 
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Express \"e%5E%28log%284%2Cx%29%29\" as a power of x. \r
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document.write( "Use the change of base formula, where NEW and OLD refer to the\r\n" );
document.write( "NEW and OLD bases:\r\n" );
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document.write( "\"log%28OLD%2C+A%29+=+log%28NEW%2CA%29%2Flog%28NEW%2COLD%29\"\r\n" );
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document.write( "We want to use that to change \"log%284%2Cx%29\" from OLD base 4 \r\n" );
document.write( "to NEW base e:\r\n" );
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document.write( "\"log%284%2Cx%29=log%28e%2Cx%29%2Flog%28e%2C4%29\"\r\n" );
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document.write( "And we realize that \"log%28e%2C%22%22%29\" is the same as \"%22ln%22\"\r\n" );
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document.write( "So\r\n" );
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document.write( "\"log%284%2Cx%29=ln%28x%29%2Fln%284%29\" \r\n" );
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document.write( "And therefore\r\n" );
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document.write( "\"e%5E%28log%284%2Cx%29%29\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"drawing%2870%2C75%2C0%2C1%2C-1%2C1%2Clocate%280%2C0%2Ce%5E%28ln%28x%29%2Fln%284%29%29%29+%29\"\r\n" );
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document.write( "We write that quotient exponent \"ln%28x%29%2Fln%284%29\" as a product \"ln%28x%29%2A%22%22\"\"1%2Fln%284%29\"\r\n" );
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document.write( "Now we use the rule \"B%5E%28A%2AC%29+=+%28B%5EA%29%5EC\"\r\n" );
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document.write( "Next we use the rule \"e%5E%28ln%28A%29%29=A\" to write the above as\r\n" );
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document.write( "and that is a power of x.\r\n" );
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document.write( "Edwin
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