document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1000305>Question 1000305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that x=ln(A) and y=ln(B) . Write the following expressions in terms of x and y (so you cannot have A or B anywhere in your answers).\r<BR>\n" );
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document.write( "ln(AB)=<BR>\n" );
document.write( "ln(A)/ln(B)=<BR>\n" );
document.write( "AB=\r<BR>\n" );
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document.write( "Please help, I do not understand these. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617761 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1. &nbsp;ln(AB) = ln(A) + ln(B) = x + y.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;First equality is the basic property of the logarithm. &nbsp;Are you familiar with it?\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The second equality is true because &nbsp;ln(A) = x &nbsp;and &nbsp;ln(B) = y, &nbsp;which is given. &nbsp;I simply made a substitution here.\r<BR>\n" );
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document.write( "2. &nbsp;ln(A)/ln(B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fy ALIGN=MIDDLE  ALT=\"x%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Simply substitute &nbsp;x&nbsp; and &nbsp;y&nbsp; instead of &nbsp;ln(A)&nbsp; and &nbsp;ln(B)&nbsp; into the numerator and denominator. \r<BR>\n" );
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document.write( "3. &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2AB ALIGN=MIDDLE  ALT=\"A%2AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > . <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ey ALIGN=MIDDLE  ALT=\"e%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Since &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29 ALIGN=MIDDLE  ALT=\"ln%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;you have &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Since &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28B%29 ALIGN=MIDDLE  ALT=\"ln%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;you have &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ey ALIGN=MIDDLE  ALT=\"e%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Then substitute this into &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2AB ALIGN=MIDDLE  ALT=\"A%2AB\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "That is all, &nbsp;my dear.\r<BR>\n" );
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document.write( "Look into my lessons \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A   rel=nofollow HREF=http://www.algebra.com/algebra/homework/logarithm/what-is-the-logarithm.lesson>WHAT IS the logarithm</A>&nbsp; \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A   rel=nofollow HREF=http://www.algebra.com/algebra/homework/logarithm/Properties-of-the-logarithm.lesson>Properties of the logarithm</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "It is free of charge and without registration.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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