document.write( "Question 43039: 
Given that 0.475 < log base 10 of 3 < 0.478, how 
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document.write( "many digits are in the number 350?  \n" );
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Algebra.Com's Answer #28065 by AnlytcPhil(1808)\"\" \"About 
You can put this solution on YOUR website!
 
Given that 0.475 < log base 10 of 3 < 0.478, how \r\n" );
document.write( "many digits are in the number 350? \r\n" );
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document.write( "We have to get 350 into the form 10x\r\n" );
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document.write( "We need to find x such that\r\n" );
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document.write( "350 = 10x\r\n" );
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document.write( "Take logs (base 10 understood) of both sides\r\n" );
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document.write( "log(350) = log(10x)\r\n" );
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document.write( "Using rules of logarithms:\r\n" );
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document.write( "50·log(3) = x\r\n" );
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document.write( "Solve for log(3)\r\n" );
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document.write( "log(3) = x/50\r\n" );
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document.write( "We are given that\r\n" );
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document.write( "0.475 < log(3) < 0.478\r\n" );
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document.write( "So substitute x/50 for log(3)\r\n" );
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document.write( "0.475 < x/50 < 0.478\r\n" );
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document.write( "Multiply thru by 50\r\n" );
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document.write( "23.75 < x < 23.9\r\n" );
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document.write( "Raise 10 to all three powers:\r\n" );
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document.write( "1023.75 < 10x < 1023.9\r\n" );
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document.write( "1023.75 < 350 < 1023.9\r\n" );
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document.write( "Integers equal to or greater than 100 but less than 101\r\n" );
document.write( "have 1 digit.\r\n" );
document.write( "Integers equal to or greater than 101 but less than 102\r\n" );
document.write( "have 2 digits.\r\n" );
document.write( "Integers equal to or greater than 102 but less than 103\r\n" );
document.write( "have 3 digits.\r\n" );
document.write( "Integers equal to or greater than 103 but less than 104\r\n" );
document.write( "have 4 digits.\r\n" );
document.write( "...      ...      ...      ...      ...      ...      ...      ...\r\n" );
document.write( "Integers equal to or greater than 1023 but less than 1024\r\n" );
document.write( "have 24 digits.\r\n" );
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document.write( "1023 < 1023.75 < 350 < 1023.9 < 1024\r\n" );
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document.write( "Thus 350 has 24 digits.\r\n" );
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document.write( "Checking with the calculator: 350 = 7.176879877×1023\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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