document.write( "Question 1193138: x=log2x-log8x=4 \n" ); document.write( "
Algebra.Com's Answer #825135 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There is no way to use methods of algebra to solve an equation for \r\n" );
document.write( "an unknown that appears both inside and outside of a logarithmic, \r\n" );
document.write( "exponential, or trigonometric function.  The only way is to \r\n" );
document.write( "approximate it with a computer, calculator, or iterative method \r\n" );
document.write( "(\"educated\" trial and error).\r\n" );
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document.write( "Perhaps you did not mean to have \" x= \" in the front as if it were\r\n" );
document.write( "part of the equation, and meant only this equation:\r\n" );
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document.write( "\"log%282%2C%28x%29%29-log%288%2C%28x%29%29\"\"%22%22=%22%22\"\"4\"\r\n" );
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document.write( "Let's convert one of the logs so we will have both logs to the same \r\n" );
document.write( "base.\r\n" );
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document.write( "I choose to convert \"log%288%2C%28x%29%29\" to base 2.\r\n" );
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document.write( "You should memorize the change of base formula:\r\n" );
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document.write( " \"log%28b%2C%28a%29%29=log%28c%2C%28a%29%29%2Flog%28c%2C%28b%29%29\"\r\n" );
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document.write( "and plug in a=x, b=8, c=2\r\n" );
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document.write( "\"log%288%2C%28x%29%29=log%282%2C%28x%29%29%2Flog%282%2C8%29\"\"%22%22=%22%22\"\"log%282%2C%28x%29%29%2Flog%282%2C2%5E3%29=log%282%2Cx%29%2F3\"\r\n" );
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document.write( "So substitute \"log%282%2C%28x%29%29%2F3\" for \"log%288%2C%28x%29%29\" in\r\n" );
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document.write( "\"log%282%2C%28x%29%29-log%288%2C%28x%29%29\"\"%22%22=%22%22\"\"4\"\r\n" );
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document.write( "\"log%282%2C%28x%29%29-log%282%2C%28x%29%29%2F3%5E%22%22%5E%22%22\"\"%22%22=%22%22\"\"4\"\r\n" );
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document.write( "Multiply through by 3\r\n" );
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document.write( "\"3log%282%2C%28x%29%29-log%282%2C%28x%29%29\"\"%22%22=%22%22\"\"12\"\r\n" );
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document.write( "\"2log%282%2C%28x%29%29\"\"%22%22=%22%22\"\"12\"\r\n" );
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document.write( "\"log%282%2C%28x%29%29\"\"%22%22=%22%22\"\"6\"\r\n" );
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document.write( "By the definition of logarithms, from the above equation,\r\n" );
document.write( "we have this:\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"%22_____%22\"\"%22%22=%22%22\"\"%22_____%22\" \r\n" );
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document.write( "(You fill in those blanks, the first one with an \r\n" );
document.write( "eponential expression and the second with a number.\r\n" );
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document.write( "Edwin
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