document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185384>Question 1185384</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If logb(2)=1.2 and logb(3)=1.5, evaluate logb(6)=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816202 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=816202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> one of the log rules says that log(a * b) = log(a) + log(b).\r<BR>\n" );
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document.write( "this rule applies regardless of the base, as long as the base is the same for all operands.\r<BR>\n" );
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document.write( "you can use your calculator to confirm this is true.\r<BR>\n" );
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document.write( "the log function of your calculator works with the base of 10.\r<BR>\n" );
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document.write( "the ln function of your calculator works with the base of e.\r<BR>\n" );
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document.write( "assume your function is log5(25).\r<BR>\n" );
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document.write( "since log5(25) = y if and only if 5^y = 25, then you know that y must be equal to 2 because 5^2 = 25.\r<BR>\n" );
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document.write( "using the base conversion formula to convert to the log function of the calculator and the ln function of the calculator, you get:\r<BR>\n" );
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document.write( "log5(25) = log(25)/log(5) = 2 and log5(25) = ln(25)/ln(2) = 2.\r<BR>\n" );
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document.write( "the log conversion formula works for any log base.\r<BR>\n" );
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document.write( "you can use this log base conversion formula to confirm that log(a * b) = log(a) + log(b).\r<BR>\n" );
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document.write( "assume a = 15 and b = 20.\r<BR>\n" );
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document.write( "a * b = 15 * 20 = 300\r<BR>\n" );
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document.write( "log(15 * 20) = log(300) = 2.477121255 if you're working in the log base of 10.\r<BR>\n" );
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document.write( "log(15) + log(20) = the same.\r<BR>\n" );
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document.write( "ln(15 * 20) = ln(300) = 5.703782475 if you're working in the log base of e.\r<BR>\n" );
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document.write( "ln(15) + ln(20) = the same.\r<BR>\n" );
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document.write( "if you're working in the base of b, you can't use you're calculator to confirm it's true, but you can be assured that the property of logs applies with the base b as well.\r<BR>\n" );
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document.write( "logb(2) = 1.2<BR>\n" );
document.write( "logb(3) = 1.5<BR>\n" );
document.write( "logb(2 * 3) = logb(2) + logb(3) = 1.2 + 1.5 = 2.7<BR>\n" );
document.write( "since 2 * 3 = 6, then logb(6) = 2.7\r<BR>\n" );
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document.write( "since the property works with all bases, than assume b = 10 and you get:\r<BR>\n" );
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document.write( "log(2) = .3010299957<BR>\n" );
document.write( "log(3) = .4771212547<BR>\n" );
document.write( "log(2 * 3) = log(6) = .7781512504<BR>\n" );
document.write( "log(2) + log(3) = the same.\r<BR>\n" );
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document.write( "your solution is that logb(6) = 1.2 and 1.5 = 2.7.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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