document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890348>Question 890348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equations in logarithmic form.<BR>\n" );
document.write( "216=6^3<BR>\n" );
document.write( "36=(1/6)^(-2)<BR>\n" );
document.write( "a=bc<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #538899 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=538899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> logarithmic form os an exponential equation is as follows:\r<BR>\n" );
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document.write( "a^b = y if and only if loga(y) = b\r<BR>\n" );
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document.write( "your first equation is:\r<BR>\n" );
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document.write( "216 = 6^3\r<BR>\n" );
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document.write( "the logarithmic form of this equation would be log6(216) = 3\r<BR>\n" );
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document.write( "the base of the log is 6.\r<BR>\n" );
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document.write( "your second equation is:\r<BR>\n" );
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document.write( "36 = (1/6)^(-2)\r<BR>\n" );
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document.write( "without any modification to this equation, the logarithmic form would be log(1/6)(36) = -2\r<BR>\n" );
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document.write( "the base of the log is (1/6)\r<BR>\n" );
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document.write( "your third equation is:\r<BR>\n" );
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document.write( "a = b^c\r<BR>\n" );
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document.write( "the logarithmic form would be logb(a) = c\r<BR>\n" );
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document.write( "the base of the log is b.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "let a = 36 and b = 6 and c = 2\r<BR>\n" );
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document.write( "you get a = b^c becoming 36 = 6^2\r<BR>\n" );
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document.write( "the log form of logb(a) = c becomes log6(36) = 2\r<BR>\n" );
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document.write( "you can use the base conversion formula to calculate this using your calculator.\r<BR>\n" );
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document.write( "you would get:\r<BR>\n" );
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document.write( "log10(36)/log10(6) = 2\r<BR>\n" );
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document.write( "now you can use your calculator to get:\r<BR>\n" );
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document.write( "2 = 2 confirming the calculations are good.\r<BR>\n" );
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document.write( "the conversation formula is:\r<BR>\n" );
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document.write( "loga(b) = logc(b) / logc(a)\r<BR>\n" );
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document.write( "the log of a number to a certain base tells you the exponent that the base has to be raised to in order to get the number.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "log10(1000) = 3\r<BR>\n" );
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document.write( "3 is the exponent that the base of 10 has to be raised to in order to get 1000.\r<BR>\n" );
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document.write( "that's where the identity comes in.\r<BR>\n" );
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document.write( "10^3 = 1000 if and only if log10(1000) = 3\r<BR>\n" );
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document.write( "log10(1000) = 3 if and only if 10^3 = 1000\r<BR>\n" );
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