document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61154>Question 61154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need helping solving this for x:<BR>\n" );
document.write( "(ln x)^3=ln x^4<BR>\n" );
document.write( "Can I rewrite it as (ln x)^3=4lnx ?<BR>\n" );
document.write( "Then can I divide both sides by lnx leaving (ln x)^2=4 ?<BR>\n" );
document.write( "Can I now square both sides leaving me with ln x=2 ?<BR>\n" );
document.write( "Now I'm not sure what to do next. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42160 by </B><A HREF=/tutors/aboutme.mpl?userid=mathick><B>mathick(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathick><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=mathick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=42160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need helping solving this for x:<BR>\n" );
document.write( "(ln x)^3=ln x^4<BR>\n" );
document.write( "Can I rewrite it as (ln x)^3=4lnx ?\r<BR>\n" );
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document.write( "<font color = \"blue\">Yes.</font>\r<BR>\n" );
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document.write( "Then can I divide both sides by lnx leaving (ln x)^2=4 ?\r<BR>\n" );
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document.write( "<font color = \"blue\">Yes, but this assumes that you're not dividing both sides by 0, i.e. that ln(x) is not 0.  This step wouldn't be valid in the case that ln(x) = 0, so this case (ln(x) = 0) needs to be treated separately.</font>\r<BR>\n" );
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document.write( "Can I now square (root) both sides leaving me with ln x=2 ?\r<BR>\n" );
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document.write( "<font color = \"blue\">Right, ln (x) = 2, and also ln(x) = -2.  (Taking the square root of both sides gives ln x = +2 and ln x = -2.)  </font>\r<BR>\n" );
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document.write( "Now I'm not sure what to do next\r<BR>\n" );
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document.write( "<font color = \"blue\">To solve ln(x) = 2 for x, exponentiate both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28ln%28x%29%29+=+e%5E2 ALIGN=MIDDLE  ALT=\"e%5E%28ln%28x%29%29+=+e%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The left side simplifies, giving one of the final answers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+e%5E2 ALIGN=MIDDLE  ALT=\"x+=+e%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The equation ln (x) = -2 can be solved similarly.\r<BR>\n" );
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document.write( "Finally, there is the case when ln(x) = 0.  This happens when x = 1.  To verify that this is a solution, you can plug it into the original equation and see if it checks out (gives a true equation).</font> </SPAN>\n" );
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