document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177448>Question 177448</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ln (sqrt x-8)=5\r<BR>\n" );
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document.write( "ln x + ln (x+3)= 1\r<BR>\n" );
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document.write( "log (x-6)= log (2x+1)\r<BR>\n" );
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document.write( "need step by step instructions on how to do each problem... please include answer as well. 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 #132515 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=132515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28sqrt%28x+-8%29%29=5 ALIGN=MIDDLE  ALT=\"ln%28sqrt%28x+-8%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29+=+a%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29+=+a%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%28x+-8%29%5E%281%2F2%29%29=5 ALIGN=MIDDLE  ALT=\"ln%28%28x+-8%29%5E%281%2F2%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now use the rule that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28a%5En%29%29+=+n%2Alog%28b%2C%28a%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28a%5En%29%29+=+n%2Alog%28b%2C%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >, any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E0 ALIGN=MIDDLE  ALT=\"a%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3E0 ALIGN=MIDDLE  ALT=\"b%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29ln%28x-8%29+=+5 ALIGN=MIDDLE  ALT=\"%281%2F2%29ln%28x-8%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x+-8%29+=+10 ALIGN=MIDDLE  ALT=\"ln%28x+-8%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now use the definition <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29+=+y ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Ey=x ALIGN=MIDDLE  ALT=\"b%5Ey=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E10+=+x+-+8 ALIGN=MIDDLE  ALT=\"e%5E10+=+x+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+e%5E10+%2B+8 ALIGN=MIDDLE  ALT=\"x+=+e%5E10+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the exact answer.  Use your calculator to get a numerical approximation if that is what you need.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28x%29+%2B+ln%28x+%2B+3%29+=+1+ ALIGN=MIDDLE  ALT=\"+ln%28x%29+%2B+ln%28x+%2B+3%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First use the rule:  The sum of the logs equals the log of the product, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28a%5B1%5D%29%29+%2B+log%28b%2C%28a%5B2%5D%29%29+=+log%28b%2C%28a%5B1%5Da%5B2%5D%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, so: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29+%2B+ln%28x+%2B+3%29+=+ln%28x%28x%2B3%29%29+=+ln%28x%5E2+%2B+3x%29+=+1 ALIGN=MIDDLE  ALT=\"ln%28x%29+%2B+ln%28x+%2B+3%29+=+ln%28x%28x%2B3%29%29+=+ln%28x%5E2+%2B+3x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now use the definition <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29+=+y ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Ey=x ALIGN=MIDDLE  ALT=\"b%5Ey=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5E2+%2B+3x%29+=+1 ALIGN=MIDDLE  ALT=\"ln%28x%5E2+%2B+3x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E1+=+e+=+x%5E2+%2B+3x ALIGN=MIDDLE  ALT=\"e%5E1+=+e+=+x%5E2+%2B+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+-+e+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+-+e+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the quadratic formula:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+3%5E2-4%281%29%28-e%29+%29%29%2F2%281%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+3%5E2-4%281%29%28-e%29+%29%29%2F2%281%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+9%2B4e+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+9%2B4e+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Again, if you need a numerical approximation, use your calculator.\r<BR>\n" );
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document.write( "Use the rule:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28a%29%29+=+log%28b%2C+%28c%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28a%29%29+=+log%28b%2C+%28c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+c ALIGN=MIDDLE  ALT=\"a+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+6+=+2x+%2B+1 ALIGN=MIDDLE  ALT=\"x+-+6+=+2x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You should be able to handle the rest of this one on your own.<BR>\n" );
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