document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21612>Question 21612</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve the logarithmic equation symbolically, log x^8=7+2 log x, we did not go over this in class? <BR>\n" );
document.write( "v/r Dean  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11526 by </B><A HREF=/tutors/aboutme.mpl?userid=NaiXLG><B>NaiXLG(18)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=NaiXLG><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=11526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ahhhh yes, logarithims, gotta love 'em...\r<BR>\n" );
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document.write( "So, you begin by writing the original question\r<BR>\n" );
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document.write( "Solve for x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+x%5E8+=+7+%2B+2log+x ALIGN=MIDDLE  ALT=\"log+x%5E8+=+7+%2B+2log+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, begin by rewriting the right logarithim as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+x%5E2 ALIGN=MIDDLE  ALT=\"log+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the properties of logarithims states that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+log+b+=+log+b%5Ea+ ALIGN=MIDDLE  ALT=\"a+log+b+=+log+b%5Ea+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So now you should have,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+x%5E8+=+7+%2B+log+x%5E2 ALIGN=MIDDLE  ALT=\"log+x%5E8+=+7+%2B+log+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Bring the right logarithim to the left, so now we have all logs on the left, and all non-logs (constants) on the right.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+x%5E8+-+log+x%5E2+=+7 ALIGN=MIDDLE  ALT=\"log+x%5E8+-+log+x%5E2+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now using yet another property of logarithims, go ahead and simplify that left side into one single log....\r<BR>\n" );
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document.write( "Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+a+-+log+b+=+log%28a%2Fb%29 ALIGN=MIDDLE  ALT=\"log+a+-+log+b+=+log%28a%2Fb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, you'll have;\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%5E8%2Fx%5E2%29+=+7 ALIGN=MIDDLE  ALT=\"log%28x%5E8%2Fx%5E2%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, use your properties of exponents to simplify that log a little more...\r<BR>\n" );
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document.write( "Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Em%2Fx%5En+=+x%5E%28m-n%29 ALIGN=MIDDLE  ALT=\"x%5Em%2Fx%5En+=+x%5E%28m-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%5E6%29+=+7 ALIGN=MIDDLE  ALT=\"log%28x%5E6%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, because the log has a base of ten, raise both sides of the equation to the tenth power....\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5Elog%28x%5E6%29+=+10%5E7 ALIGN=MIDDLE  ALT=\"10%5Elog%28x%5E6%29+=+10%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The log cancels out, and you're left with\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6+=+10%5E7 ALIGN=MIDDLE  ALT=\"x%5E6+=+10%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now simply take the 6th root of x to make it just a single x, and no more, and take the 6th root of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E7 ALIGN=MIDDLE  ALT=\"10%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > as well. (What you do to one side of the equation, you must do to the other.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10%5E%287%2F6%29 ALIGN=MIDDLE  ALT=\"x+=+10%5E%287%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There you go....!\r<BR>\n" );
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