document.write( "Question 816208: How do you solve for x: log4(3x+5) = log2(4x-3) \n" ); document.write( "
Algebra.Com's Answer #491423 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "log4(3x+5) = log2(4x-3)\r\n" );
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document.write( "Let each side equal to y         \r\n" );
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document.write( "log4(3x+5) = y      and      log2(4x-3) = y\r\n" );
document.write( "        4y = 3x+5   and              2y = 4x-3\r\n" );
document.write( "     (22)y = 3x+5   \r\n" );
document.write( "       22y = 3x+5\r\n" );
document.write( "      2y·2 = 3x+5\r\n" );
document.write( "     (2y)2 = 3x+5\r\n" );
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document.write( "Substitute 4x-3 for 2y\r\n" );
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document.write( "      (4x-3)² = 3x+5\r\n" );
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document.write( "   16x²-24x+9 = 3x+5\r\n" );
document.write( "   16x²-27x+4 = 0\r\n" );
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document.write( "x = \"%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+\" \r\n" );
document.write( "x = \"%28-%28-27%29+%2B-+sqrt%28+%28-27%29%5E2-4%2816%29%284%29+%29%29%2F%282%2816%29%29+\"\r\n" );
document.write( "x = \"%2827+%2B-+sqrt%28729-256%29%29%2F32+\"\r\n" );
document.write( "x = \"%2827+%2B-+sqrt%28473%29%29%2F32+\"\r\n" );
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document.write( "Using a calculator:\r\n" );
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document.write( "x = 1.523392599 and .1641074009\r\n" );
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document.write( "only x = 1.523392599 checks.  The other answer causes the right side\r\n" );
document.write( "to give the log of a negative number, which is not a real number.\r\n" );
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document.write( "Edwin
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