document.write( "Question 770321: Given 2^x=3^y=5^z=900^w
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Algebra.Com's Answer #469479 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Given 2^x=3^y=5^z=900^w
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\n" ); document.write( "xyz=2w(xy+yz+xz)
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document.write( "Suppose that\r\n" );
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document.write( "2x = 3y = 5z = 900w = A\r\n" );
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document.write( "Then (you can also use log instead of ln, as above):\r\n" );
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document.write( "log(2x) = log(3y) = log(5z) = log(900w) = log(A)\r\n" );
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document.write( "x·log(2) = y·log(3) = z·log(5) = w·log(900) = log(A)\r\n" );
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document.write( "\"x=log%28A%29%2Flog%282%29\", \"y=log%28A%29%2Flog%283%29\", \"z=log%28A%29%2Flog%285%29\", \"w=log%28A%29%2Flog%28900%29\"\r\n" );
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document.write( "*** xyz = \"log%28A%29%2Flog%282%29\"\"%22%22%2A%22%22\"\"log%28A%29%2Flog%283%29\"\"%22%22%2A%22%22\"\"log%28A%29%2Flog%285%29\" = \"%28log%28A%29%29%5E3%2F%28log%282%29log%283%29log%285%29%29\"***\r\n" );
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document.write( "xy = \"%28log%28A%29%2Flog%282%29%29\"\"%22%22%2A%22%22\"\"%28log%28A%29%2Flog%283%29%29\" = \"%28log%28A%29%29%5E2%2F%28log%282%29log%283%29%29\"\r\n" );
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document.write( "yz = \"%28log%28A%29%2Flog%283%29%29\"\"%22%22%2A%22%22\"\"%28log%28A%29%2Flog%285%29%29\" = \"%28log%28A%29%29%5E2%2F%28log%283%29log%285%29%29\"\r\n" );
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document.write( "xz = \"%28log%28A%29%2Flog%282%29%29\"\"%22%22%2A%22%22\"\"%28log%28A%29%2Flog%285%29%29\" = \"%28log%28A%29%29%5E2%2F%28log%282%29log%285%29%29\"\r\n" );
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document.write( "xy + yz + xz = \"%28log%28A%29%29%5E2%2F%28log%282%29log%283%29%29\"\"%22%22%2B%22%22\"\"%28log%28A%29%29%5E2%2F%28log%282%29log%283%29%29\"\"%22%22%2B%22%22\"\"%28log%28A%29%29%5E2%2F%28log%282%29log%283%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "          \"%22%22=%22%22\"\r\n" );
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document.write( "\"w\"\"%22%22=%22%22\"\"log%28A%29%2Flog%28900%29\"\"%22%22=%22%22\"\"log%28A%29%2Flog%282%5E2%2A3%5E2%2A5%5E2%29\"\"%22%22=%22%22\"\"log%28A%29%2F%28log%282%5E2%29%2Blog%283%5E2%29%2Blog%285%5E2%29%29\"\"%22%22=%22%22\"\"log%28A%29%2F%282log%282%29%2B2log%283%29%2B2log%285%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "          \"log%28A%29%2F%282%28log%282%29%2Blog%283%29%2Blog%285%29%29%29\"\r\n" );
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document.write( "So 2w = \"2log%28A%29%2F%282%28log%282%29%2Blog%283%29%2Blog%285%29%29%29\"\"%22%22=%22%22\"\"cross%282%29log%28A%29%2F%28cross%282%29%28log%282%29%2Blog%283%29%2Blog%285%29%29%29\"\"%22%22=%22%22\"\"log%28A%29%2F%28log%282%29%2Blog%283%29%2Blog%285%29%29\"\r\n" );
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document.write( "2w(xy+yz+xz)\"%22%22=%22%22\"\"log%28A%29%2F%28log%282%29%2Blog%283%29%2Blog%285%29%29\"\"%22%22%2A%22%22\"\"%22%22=%22%22\"\r\n" );
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document.write( "          \"log%28A%29%2F%28cross%28log%282%29%2Blog%283%29%2Blog%285%29%29%29\"\"%22%22%2A%22%22\"\"%22%22=%22%22\"\"%28log%28A%29%29%5E3%2F%28log%282%29log%283%29log%285%29%29\"\r\n" );
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document.write( "And that's what xyz was shown equal to above, marked ***\r\n" );
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document.write( "Edwin

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