document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042488>Question 1042488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Approximate the logarithm using the properties of logarithms, given logb2=.3562, logb3=.5646, logb5=.8271\r<BR>\n" );
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document.write( "logb 12<BR>\n" );
document.write( "logb (5b^4)<BR>\n" );
document.write( "logb ^8sqrt(3b) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657464 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=657464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> logb(2) = .3562<BR>\n" );
document.write( "logb(3) = .5646<BR>\n" );
document.write( "logb(5) = .8271\r<BR>\n" );
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document.write( "logb(x) = y if and only if b^y = x.\r<BR>\n" );
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document.write( "using this formula:\r<BR>\n" );
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document.write( "logb(2) = .3562 if and only if b^.3562 = 2<BR>\n" );
document.write( "raise each side of the equation to the 1/.3562 power and you get:<BR>\n" );
document.write( "(b^(.3562)^(1/.3562) = 2^(1/.3562)<BR>\n" );
document.write( "simplify to get b = 7.000274846\r<BR>\n" );
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document.write( "do the same with the the other two and you will get b = 6.999...\r<BR>\n" );
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document.write( "since b has to the same value in all 3, then my guess is that b = 7.\r<BR>\n" );
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document.write( "using that guess, i got the answers indicated when i rounded to 4 decimal places.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "log7(2) = .3562<BR>\n" );
document.write( "log7(2) = log(2)/log(7) = .3562<BR>\n" );
document.write( "evaluate log(2)/log(7) and you get .356207.....<BR>\n" );
document.write( "round it to 4 decimal places and you get .3562.\r<BR>\n" );
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document.write( "i was able to get the other answers as well rounded to 4 decimal places when i assumed b = 7.\r<BR>\n" );
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document.write( "given that b = 7, the other problems should fall in line.\r<BR>\n" );
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document.write( "logb(12) becomes log7(12) which becomes log(12)/log(7) which is equal to 1.276989... which becomes 1.2770 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "logb(5b^4) becomes log7(5*7^4) which becomes log7(5*2401) which becomes log7(12005) which becomes log(12005)/log(7) which is equal to 4.8270874...which becomes 4.8271 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "logb ^8sqrt(3b) ?????\r<BR>\n" );
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document.write( "i'm not exactly sure what to do with this.<BR>\n" );
document.write( "did you mean logb(8*sqrt(3b)), or did you mean:<BR>\n" );
document.write( "logb^8(sqrt(3b)) ?????\r<BR>\n" );
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document.write( "what is the base?<BR>\n" );
document.write( "what is the argument of the log?\r<BR>\n" );
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document.write( "in logb(x), b is the base, and x is the argument of the log.\r<BR>\n" );
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document.write( "if you can't do that, then give it in english, such as log of (sqrt(3b)) to the base of b.\r<BR>\n" );
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document.write( "as it stand, i just can't figure it out.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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