document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890808>Question 890808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write each expression in terms of common logarithms, and then give a calculator approximation (correct to four decimal places).<BR>\n" );
document.write( "(a)log8(10)<BR>\n" );
document.write( "exact value<BR>\n" );
document.write( "(b)log6 (302)<BR>\n" );
document.write( "exact value </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539281 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> LOG = log to the base of 10 that your calculator can handle.<BR>\n" );
document.write( "LN = log to the base of e that your calcjulator can  handle.<BR>\n" );
document.write( "most scientific calculators can handle both of these.<BR>\n" );
document.write( "convert to one or the other and you can find the log using your calculator.\r<BR>\n" );
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document.write( "log8(10) = LOG(10) / LOG(8)\r<BR>\n" );
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document.write( "log8(10) = LN(10) / LN(8)\r<BR>\n" );
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document.write( "both will get you the same answer.\r<BR>\n" );
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document.write( "log6(302) = LOG(302) / LOG(6)\r<BR>\n" );
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document.write( "log6(302) = LN(302) / LN(6)\r<BR>\n" );
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document.write( "both will get you the same answer.\r<BR>\n" );
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document.write( "LOG(10)/LOG(8) = LN(10)/LN(8) = 1.107309365 = 1.1073 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "LOG(302)/LOG(6) = LN(302)/LN(6) = 3.187050001 = 3.1871 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "those answers are exact to the best ability of the calculator.<BR>\n" );
document.write( "they could contain more decimal places than shown on the display.<BR>\n" );
document.write( "they do not appear to be rational although i can't tell for sure.<BR>\n" );
document.write( "the calculator couldn't give me an equivalent expression in terms of fractions so i'm assuming they are irrational and can't be displayed as a ratio of 2 integers.\r<BR>\n" );
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document.write( "in exponential form, the 2 expressions would look like this:\r<BR>\n" );
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document.write( "log8(10) = y if and only if 8^y = 10\r<BR>\n" );
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document.write( "log6(302) = y if and only if 6^y = 302\r<BR>\n" );
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document.write( "to solve for y, you would have to convert them back to logs again.\r<BR>\n" );
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document.write( "you will wind up with the conversion formula in both cases.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "8^y = 10<BR>\n" );
document.write( "take log of both sides to get:<BR>\n" );
document.write( "LOG(8^y) = LOG(10)<BR>\n" );
document.write( "since LOG(8^y) = y*LOG(8), equation becomes:<BR>\n" );
document.write( "y*LOG(8) = LOG(10)<BR>\n" );
document.write( "divide both sides of equation by LOG(8) to get:<BR>\n" );
document.write( "y = LOG(10)/LOG(8)<BR>\n" );
document.write( "that's the same as using the log of any base to LOG conversion formula.<BR>\n" );
document.write( "that formula is:<BR>\n" );
document.write( "logb(x) = LOG(x)/LOG(b)<BR>\n" );
document.write( "it's the same formula we used up top.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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