document.write( "Question 1002287: Hi,
\n" ); document.write( "I really really need to submit my math homeworks as soon as possible, but I cant solve this one question. I need your help. Thank you so much in advance. :)\r
\n" ); document.write( "\n" ); document.write( "2^(2x) - 2^(x+2) = 32 \n" ); document.write( "
Algebra.Com's Answer #619217 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"2%5E%282x%29+-+2%5E%28x%2B2%29+=+32\"\r\n" );
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document.write( "Use the laws of exponents \r\n" );
document.write( "        \"%28a%5Eb%29%5Ec=a%5E%28bc%29\" and \"a%5Eb%2Aa%5Ec=a%5E%28b%2Bc%29\"\r\n" );
document.write( "in reverse as\r\n" );
document.write( "        \"a%5E%28bc%29=%28a%5Eb%29%5Ec\" and \"a%5E%28b%2Bc%29=a%5Eb%2Aa%5Ec\"\r\n" );
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document.write( "to rewrite the terms on the left of\r\n" );
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document.write( "\"2%5E%282x%29+-+2%5E%28x%2B2%29+=+32\"\r\n" );
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document.write( "as\r\n" );
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document.write( "\"%282%5Ex%29%5E2+-+2%5Ex%2A2%5E2+=+32\"\r\n" );
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document.write( "\"%282%5Ex%29%5E2+-+2%5Ex%2A4+=+32\"\r\n" );
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document.write( "\"%282%5Ex%29%5E2+-+4%282%5Ex%29+=+32\"\r\n" );
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document.write( "\"%282%5Ex%29%5E2+-+4%282%5Ex%29-+32=0\"\r\n" );
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document.write( "Let u = 2x\r\n" );
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document.write( "\"u%5E2-4u-32=0\"\r\n" );
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document.write( "Factor the left side:\r\n" );
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document.write( "\"%28u-8%29%28u%2B4%29=0\"\r\n" );
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document.write( "u-8 = 0;   u+4 = 0\r\n" );
document.write( "  u = 8;     u = -4\r\n" );
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document.write( "Since u = 2x\r\n" );
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document.write( "2x = 8;  2x = -4\r\n" );
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document.write( "The second has no real solution so we ignore it.\r\n" );
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document.write( "2x = 8\r\n" );
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document.write( "2x = 23\r\n" );
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document.write( "The bases are equal and positive and not 1, so \r\n" );
document.write( "the exponents are equal.\r\n" );
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document.write( "x = 3\r\n" );
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document.write( "Edwin

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