Algebra.Com's Answer #831117 by ikleyn(52797)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Find the smallest positive integer n such that the base ten representation
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document.write( "of 2 at the power of n has exactly 500 digits.
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document.write( "We want to find smallest possible integer n in such a way that\r\n" );
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document.write( "  >=  (notice that is the smallest integer number requiring 500 digits in base 10).\r\n" );
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document.write( "So, we have this simple inequality. To solve it, take logarithm base 10 of both sides. \r\n" );
document.write( "You will get this inequality\r\n" );
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document.write( " n*log(2) >= 499\r\n" );
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document.write( " n >=  = now use your calculator = 1657.642 (rounded).\r\n" );
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document.write( "To get that integer n, you must round the decimal 1657.642 to the nearest greater integer, which is, by the case, 1658.\r\n" );
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document.write( "ANSWER. 1658 is the smallest positive integer n such that the base ten representation \r\n" );
document.write( " of 2 at the power of n has exactly 500 digits.\r\n" );
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document.write( "Solved, with complete explanations.\r
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