document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999930>Question 999930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am particular to doing the e^ln to each side of a number. And this problem is troublesome. \r<BR>\n" );
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document.write( "I want to find the answer to: <BR>\n" );
document.write( "1/10 = (1/2)^(30/h) \r<BR>\n" );
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document.write( "I keep running into problems, since there is an exponential on one side, I take the e to the ln of each side like so: \r<BR>\n" );
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document.write( "e^ln(1/10) = e^(ln(1/2)^(30/h)) <BR>\n" );
document.write( "e^ln(1/10) = e^((30/h)ln(1/2)) <BR>\n" );
document.write( "Then since anything to the e^ln cancels for both sides: <BR>\n" );
document.write( "1/10 = (30/h)(1/2) <BR>\n" );
document.write( "Something doesn't smell right here. What did I do wrong and how can I get the correct answer of h = 9.03 \r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617460 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Okay, from<BR>\n" );
document.write( "1/10 = (1/2)^(30/h) <BR>\n" );
document.write( "you just take the ln first...<BR>\n" );
document.write( "ln(1/10) = ln[(1/2)^(30/h)]<BR>\n" );
document.write( "ln(1/10) = (30/h)ln(1/2) <BR>\n" );
document.write( "since ln(1/x) = -ln x, we get<BR>\n" );
document.write( "-ln10 = (30/h)(-ln2)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "30/h = -ln10/-ln2 = ln10/ln2<BR>\n" );
document.write( "and rearranging gives<BR>\n" );
document.write( "h = 30/(ln10/ln2) = 30 ln 2 / ln 10 = 9.03 </SPAN>\n" );
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