document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147076>Question 1147076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine logarithm of 59,436.\r<BR>\n" );
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document.write( "My attempt:\r<BR>\n" );
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document.write( "log 594 = 7738 (table).\r<BR>\n" );
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document.write( "4.7738\r<BR>\n" );
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document.write( "10^4.7738 = 59401.\r<BR>\n" );
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document.write( "Where did I miscalculate?  Non-homework.\r<BR>\n" );
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document.write( "No miscalculation.  If you use the table to find log(594) = 0.7738, then 10^4.7738 will be approximately 59400, which is what you found.<br><BR>\n" );
document.write( "If you want a more accurate answer, you need to interpolate between the values given in the table.<br><BR>\n" );
document.write( "Over very short intervals, the graph of a logarithm is nearly linear, so you can use linear interpolation.<br><BR>\n" );
document.write( "log(594) = .7738<BR>\n" );
document.write( "log(595) = .7745<br><BR>\n" );
document.write( "The difference is .0007.  Then a good approximation is<br><BR>\n" );
document.write( "log(59436) = .7738 + .36(.0007) = .77405<br><BR>\n" );
document.write( "Then using a calculator we find<br><BR>\n" );
document.write( "10^4.77405 = 59436<br><BR>\n" );
document.write( "to the nearest whole number -- which is what we want. </SPAN>\n" );
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