document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210603>Question 1210603</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I came across this in an old book:\r<BR>\n" );
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document.write( "Determine logarithm of 6253.\r<BR>\n" );
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document.write( "In table, the mantissa is .7959 (The same mantissa of 6250).   The next larger is .7966, mantissa of 6260.\r<BR>\n" );
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document.write( "6260 - 6250 = 10 (difference of 10).\r<BR>\n" );
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document.write( ".7966 - .7959 = 0.0007\r<BR>\n" );
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document.write( "This is part I don't understand:\r<BR>\n" );
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document.write( "Each increase of 1 unit (6250 increase of 10 to 6260), mantissas of their logs increase by 0.0007, an increase of .1 of 0.0007. 3 added to 0250 will add .3 of 0.0007 or 0.0002 to the mantissa of 6253.  \r<BR>\n" );
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document.write( "Why is .1 and .3 added ? </SPAN>\n" );
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document.write( "The wording here (as you show it) is not at all clear:<br><BR>\n" );
document.write( "\"Each increase of 1 unit (6250 increase of 10 to 6260), mantissas of their logs increase by 0.0007, an increase of .1 of 0.0007. 3 added to 0250 will add .3 of 0.0007 or 0.0002 to the mantissa of 6253.\"<br><BR>\n" );
document.write( "If that is actually the way the problem was presented to you, it is not surprising that you don't understand.<br><BR>\n" );
document.write( "The table gives us log(6250) = 3.7959 and log(6260) = 3.7966.<br><BR>\n" );
document.write( "To determine log(6253), we need to interpolate.<br><BR>\n" );
document.write( "For a small change in the number, the change in the logarithm is approximately linear.<br><BR>\n" );
document.write( "In this example, a change of 10 (from 6250 to 6260) in the number produces a change of .0007 (from 3.7959 to 3.7966) in the logarithm.  Since 6253 is 3/10 of the distance from 6250 to 6260, the logarithm of 6253 is 3/10 of the way from log(6250) to log(6260).<br><BR>\n" );
document.write( "3/10 of .0007 is .00021, so log(6253) is log(6250) + .00021 = 3.7959 + .00021 = 3.79611.<br><BR>\n" );
document.write( "But since the logarithms in the table are given to only 4 decimal places, we probably don't want to have more than 4 decimal places in our answer.  So<br><BR>\n" );
document.write( "ANSWER: log(6253) = 3.7961<br><BR>\n" );
document.write( "(Or, if the problem asks you only for the mantissa of the logarithm, then the answer is just 0.7961)<br><BR>\n" );
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