document.write( "Question 978245: Solve and leave answer in interval notation. (1/4)^3x<6^x-2 \n" ); document.write( "
Algebra.Com's Answer #599717 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%281%2F4%29%5E%283x%29\"\"%22%22%3C%22%22\"\"6%5E%28x-2%29\"\r\n" );
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document.write( "Take logs of both sides:\r\n" );
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document.write( "\"log%28%281%2F4%29%5E%283x%29%29\"\"%22%22%3C%22%22\"\"log%28%286%5E%28x-2%29%29%29\"\r\n" );
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document.write( "\"3x%2Alog%28%281%2F4%29%29%29\"\"%22%22%3C%22%22\"\"%28x-2%29%2Alog%28%286%29%29%29\"\r\n" );
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document.write( "Let \"log%28%281%2F4%29%29=A\" and \"log%28%286%29%29=B\"\r\n" );
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document.write( "\"3x%2AA\"\"%22%22%3C%22%22\"\"%28x-2%29%2AB\"\r\n" );
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document.write( "\"3Ax\"\"%22%22%3C%22%22\"\"B%28x-2%29\"\r\n" );
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document.write( "\"3Ax\"\"%22%22%3C%22%22\"\"Bx-2B\"\r\n" );
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document.write( "\"3Ax-Bx\"\"%22%22%3C%22%22\"\"-2B\"\r\n" );
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document.write( "\"x%283A-B%29\"\"%22%22%3C%22%22\"\"-2B\"\r\n" );
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document.write( "Now we will divide through by (3A-B), but first we must calculate \r\n" );
document.write( "3A-B to find out whether we are dividing by a positive or a negative\r\n" );
document.write( "so that we will know whether or not we must flip the inequality\r\n" );
document.write( "symbol from < to > or leave it as it is.\r\n" );
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document.write( "\"3A-B=3log%28%281%2F4%29%29-log%28%286%29%29=B\" = -2.584331224 which is negative\r\n" );
document.write( "so we must flip the inequality symbol:\r\n" );
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document.write( "\"x\"\"%22%22%3E%22%22\"\"%28-2B%29%2F%283A-B%29\"\r\n" );
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document.write( "Substitute \"A=log%28%281%2F4%29%29\" and \"B=log%28%286%29%29\"\r\n" );
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document.write( "\"x\"\"%22%22%3E%22%22\"\"%28-2log%28%286%29%29%29%2F%283log%28%281%2F4%29%29-log%28%286%29%29%29\"\r\n" );
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document.write( "\"x\"\"%22%22%3E%22%22\"\"0.6022070569\"\r\n" );
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document.write( "\"%28matrix%281%2C3%2C0.6022070569%2C%22%2C%22%2Cinfinity%29%29\"\r\n" );
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document.write( "Edwin
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