document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148108>Question 1148108</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Given: log5=a, log3=b,log2=c. Find: log_30(8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #769482 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=769482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are given:\r<BR>\n" );
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document.write( "log(5) = a<BR>\n" );
document.write( "log(3) = b<BR>\n" );
document.write( "log(2) = c\r<BR>\n" );
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document.write( "you want to find log_30(8).<BR>\n" );
document.write( "you can use the log base conversion formula to get:<BR>\n" );
document.write( "log_30(8) = log(8) / log(30)\r<BR>\n" );
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document.write( "we start with log_30(8) = log(8) / log(30).<BR>\n" );
document.write( "8 is equal to 2^3 and 30 is equal to 5 * 3 * 2, so the formula becomes:<BR>\n" );
document.write( "log_30(8) = log(2^3) / log(5 * 3 * 2)<BR>\n" );
document.write( "by the rules of logarithms, this becomes:<BR>\n" );
document.write( "log_30(8) = 3 * log(2) / (log(5) + log(3) + log(2))<BR>\n" );
document.write( "since log(5) = a and log(3) = b and log(2) = c, we get:<BR>\n" );
document.write( "log_30(8) = (3 * c) / (a + b + c)\r<BR>\n" );
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document.write( "your answer should be:\r<BR>\n" );
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document.write( "log_30(8) = (3 * c) / (a + b + c)\r<BR>\n" );
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document.write( "to see if that's true, we replace a, b, c with their respective values of:<BR>\n" );
document.write( "a = log(5)<BR>\n" );
document.write( "b = log(3)<BR>\n" );
document.write( "c = log(2)<BR>\n" );
document.write( "to get:<BR>\n" );
document.write( "log_30(8) = 3 * log(2) / (log(5) + log(3) + log(2)) = .6113851413.\r<BR>\n" );
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document.write( "you can use your calculator to see that log(8) / log(30) = the same value.\r<BR>\n" );
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document.write( "you can also use your calculator to see that log_30(8) = .6113851413 if and only if 30 ^ .6113851413 = 8.<BR>\n" );
document.write( "it did equal that on my calculator.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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