document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1059970>Question 1059970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> good morning\r<BR>\n" );
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document.write( "would you help me find the logarithmic equation\r<BR>\n" );
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document.write( "6+ln(8x)=24-2 ln(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675020 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=675020\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve for x over the real numbers<BR>\n" );
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document.write( "6 + ln(8x) = 24 - 2ln(x)<BR>\n" );
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document.write( "Subtract 24 - 2 ln(x) from both sides<BR>\n" );
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document.write( "-18 + 2ln(x) + ln(8x) = 0<BR>\n" );
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document.write( "-18 + 2ln(x) + ln(8x) = -18 + ln(8x) + ln(x^2) = ln(8x^3) - 18<BR>\n" );
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document.write( "Note that c(ln(x)) = ln(x^c) where c is a constant, then we use the product rule of logarithms<BR>\n" );
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document.write( "ln(8x^3) - 18 = 0<BR>\n" );
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document.write( "Add 18 to both sides<BR>\n" );
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document.write( "ln(8x^3) = 18<BR>\n" );
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document.write( "Cancel logarithms by taking exp of both sides, note that ln is natural logarithm<BR>\n" );
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document.write( "8x^3 = e^18<BR>\n" );
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document.write( "Divide both sides by 8<BR>\n" );
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document.write( "x^3 = e^18/8<BR>\n" );
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document.write( "Take cube roots of both sides<BR>\n" );
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document.write( "x = e^6/2<BR>\n" );
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document.write( "Note that e is approximately 2.71828<BR>\n" );
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document.write( "x = (2.71828)^6 / 2 is approximately 201.7144 <BR>\n" );
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