document.write( "Question 966454: 2^2x+3=3^3x\r
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Algebra.Com's Answer #590680 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor interpreted it wrong.  You should always enclose \r\n" );
document.write( "exponents that consist of more than 1 letter or number in parentheses.\r\n" );
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document.write( "\"2%5E%282x%2B3%29=3%5E%283x%29\"\r\n" );
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document.write( "Take logs of both sides:\r\n" );
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document.write( "\"log%28%282%5E%282x%2B3%29%29%29=log%28%283%5E%283x%29%29%29\"\r\n" );
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document.write( "Ues the \"exponent leaps over log\" formula \"log%28%28B%5EA%29%29=A%2Alog%28%28B%29%29\"\r\n" );
document.write( "on both sides\r\n" );
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document.write( "\"%282x%2B3%29log%28%282%29%29=3x%2Alog%28%283%29%29\"\r\n" );
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document.write( "To make it easier to see, \r\n" );
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document.write( "Let A = log(2) and B = log(3)\r\n" );
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document.write( "\"%282x%2B3%29A=3x%2AB\"\r\n" );
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document.write( "\"A%282x%2B3%29=3Bx\"\r\n" );
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document.write( "\"2Ax%2B3A=3Bx\"\r\n" );
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document.write( "Get all the terms in x on one side, and all the non-x terms\r\n" );
document.write( "on the other.  I'll pick the right side for the x terms:\r\n" );
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document.write( "\"3A=3Bx-2Ax\"\r\n" );
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document.write( "Factor out x on the right\r\n" );
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document.write( "\"3A=x%283B-2A%29\"\r\n" );
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document.write( "Divide both sides by (3B-2A)\r\n" );
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document.write( "\"%283A%29%2F%283B-2A%29=x\"\r\n" );
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document.write( "Now substitute log(2) for A and log(3) for B\r\n" );
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document.write( "\"%283log%28%282%29%29%29%2F%283log%28%283%29%29-2log%28%282%29%29%29%7D%7D%29=x\"\r\n" );
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document.write( "x = 1.088973687\r\n" );
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document.write( "Edwin
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