document.write( "Question 1144759: Given 2^m × (1/8)^n = 128 and 4^m ÷ 2^(-4n) = 1/6, find the value of (m-n). \n" ); document.write( "
Algebra.Com's Answer #766040 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"system%282%5Em%2A%281%2F8%29%5En+=+128%2C+4%5Em%2F2%5E%28-4n%29+=+1%2F6%29\"\r\n" );
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document.write( "\"system%28+2%5Em%2A%288%5E%28-1%29%29%5En+=+2%5E7%2C+4%5Em%2A2%5E%284n%29+=+1%2F6%29\"\r\n" );
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document.write( "\"system%282%5Em%2A8%5E%28-n%29+=+2%5E7%2C+%282%5E2%29%5Em%2A2%5E%284n%29+=+1%2F6%29\"\r\n" );
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document.write( "\"system%282%5Em%2A%282%5E3%29%5E%28-n%29+=+2%5E7%2C+2%5E%282m%29%2A2%5E%284n%29+=+1%2F6%29\"\r\n" );
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document.write( "\"system%282%5Em%2A2%5E%28-3n%29+=+2%5E7%2C+2%5E%282m%2B4n%29+=+1%2F6%29\"\r\n" );
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document.write( "\"system%282%5E%28m-3n%29+=+2%5E7%2C+2%5E%282m%2B4n%29+=+1%2F6%29\"\r\n" );
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document.write( "\"system%28m-3n+=+7%2C+2%5E%282m%2B4n%29+=+1%2F6%29\"\r\n" );
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document.write( "\"system%28m=3n%2B7%2C+2%5E%282m%2B4n%29+=+1%2F6%29\"\r\n" );
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document.write( "By substitution:\r\n" );
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document.write( "\"2%5E%282%283n%2B7%29%2B4n%29+=+1%2F6\"\r\n" );
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document.write( "\"2%5E%2810n%2B14%29+=+1%2F6\"\r\n" );
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document.write( "Multiply both sides by 2\r\n" );
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document.write( "\"2%2A2%5E%2810n%2B14%29+=+2%2Aexpr%281%2F6%29\"\r\n" );
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document.write( "\"2%5E%2810n%2B14%2B1%29+=+1%2F3\"\r\n" );
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document.write( "\"2%5E%2810n%2B15%29+=+3%5E%28-1%29\"\r\n" );
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document.write( "Take natural logs of both sides:\r\n" );
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document.write( "\"ln%282%5E%2810n%2B15%29%29+=+ln%283%5E%28-1%29%29\"\r\n" );
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document.write( "\"%2810n%2B15%29ln%282%29+=+-ln%283%29\"\r\n" );
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document.write( "Divide both sides by ln(2)\r\n" );
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document.write( "\"10n%2B15=-ln%283%29%2Fln%282%29\"\r\n" );
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document.write( "\"10n=-15-ln%283%29%2Fln%282%29\"\r\n" );
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document.write( "Multiply both sides by 1/10\r\n" );
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document.write( "\"n=expr%281%2F10%29%28-15-ln%283%29%2Fln%282%29%29\"\r\n" );
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document.write( "\"m=3n%2B7\"\r\n" );
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document.write( "\"m=expr%283%2F10%29%28-15-ln%283%29%2Fln%282%29%29%2B7\"\r\n" );
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document.write( "But you don't want m or n, you want m-n\r\n" );
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document.write( "\"m-n=expr%282%2F10%29%28-15-ln%283%29%2Fln%282%29%29%2B7\"\r\n" );
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document.write( "\"m-n=expr%281%2F5%29%28-15-ln%283%29%2Fln%282%29%29%2B7\"\r\n" );
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document.write( "Edwin
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