document.write( "Question 63517: 
Hi I am having problems with this: Solve the following equation:\r\n" );
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document.write( "3x = 15·4x-2
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Algebra.Com's Answer #44196 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Hi I am having problems with this: Solve the following equation:\r\n" );
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document.write( "3x = 15·4x-2\r\n" );
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document.write( "We need two rules of natural logarithms:\r\n" );
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document.write( "(1)   ln(AB) = ln(A) + ln(B)\r\n" );
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document.write( "(2)   ln(AN) = N·ln(A) \r\n" );
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document.write( "          3x = 15·4x-2\r\n" );
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document.write( "Take the natural logarithm of both sides:\r\n" );
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document.write( "      ln(3x) = ln(15·4x-2)\r\n" );
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document.write( "Use rule (2) on the left side and rule (1) on\r\n" );
document.write( "the right side:\r\n" );
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document.write( "     x·ln(3) = ln(15) + ln(4x-2)\r\n" );
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document.write( "Use rule (2) on the last term on the right \r\n" );
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document.write( "     x·ln(3) = ln(15} + (x-2)·ln(4)\r\n" );
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document.write( "To make things easier, let\r\n" );
document.write( "A = ln(3), B = ln(15) and C = ln(4)\r\n" );
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document.write( "         x·A = B + (x-2)·C \r\n" );
document.write( "          Ax = B + C(x-2)\r\n" );
document.write( "          Ax = B + Cx - 2C\r\n" );
document.write( "     Ax - Cx = B - 2C\r\n" );
document.write( "    x(A - C) = B - 2C\r\n" );
document.write( "           x = (B - 2C)/(A - C)\r\n" );
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document.write( "Now replace A by ln(3), B by ln(15), \r\n" );
document.write( "and C by ln(4):\r\n" );
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document.write( "           x = [ln(15)-2·ln(4)]/[ln(3)-ln(4)]\r\n" );
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document.write( "Now get your calculator and get:\r\n" );
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document.write( "           x = .2243397393\r\n" );
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document.write( "Edwin

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