document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=948326>Question 948326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> D1: Let’s combine our knowledge of solving systems and solving logarithmic equations. Solve the system of equations: <BR>\n" );
document.write( "log yx = 3, this is log with a base of y, then x equals 3.<BR>\n" );
document.write( "log y&#8201;(4x) = 5, this is log with a base of y,(4x) equals 5.\r<BR>\n" );
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document.write( "I am trying to figure this question out. I need steps involved please.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578825 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=578825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28y%2Cx%29+=+3 ALIGN=MIDDLE  ALT=\"log+%28y%2Cx%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...change the base to base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   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=log+%28x%29%2Flog+%28y%29+=+3 ALIGN=MIDDLE  ALT=\"log+%28x%29%2Flog+%28y%29+=+3\"   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=log+%28x%29+=+3log+%28y%29 ALIGN=MIDDLE  ALT=\"log+%28x%29+=+3log+%28y%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=log+%28x%29+=+log+%28y%5E3%29 ALIGN=MIDDLE  ALT=\"log+%28x%29+=+log+%28y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...if log same, then we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+y%5E3 ALIGN=MIDDLE  ALT=\"x+=+y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...........eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28y%2C%284x%29%29+=+5 ALIGN=MIDDLE  ALT=\"log+%28y%2C%284x%29%29+=+5\"   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=log+%28%284x%29%29%2Flog+%28y%29+=+5 ALIGN=MIDDLE  ALT=\"log+%28%284x%29%29%2Flog+%28y%29+=+5\"   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=log+%28%284x%29%29+=+5log+%28y%29 ALIGN=MIDDLE  ALT=\"log+%28%284x%29%29+=+5log+%28y%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=log+%28%284x%29%29+=+log+%28y%5E5%29 ALIGN=MIDDLE  ALT=\"log+%28%284x%29%29+=+log+%28y%5E5%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=4x+=+y%5E5 ALIGN=MIDDLE  ALT=\"4x+=+y%5E5\"   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+=+y%5E5%2F4 ALIGN=MIDDLE  ALT=\"x+=+y%5E5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............eq.2\r<BR>\n" );
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document.write( "system is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+y%5E3 ALIGN=MIDDLE  ALT=\"x+=+y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...........eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+y%5E5%2F4 ALIGN=MIDDLE  ALT=\"x+=+y%5E5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............eq.2\r<BR>\n" );
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document.write( "since left sides same, right sides must be equal too\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3=y%5E5%2F4 ALIGN=MIDDLE  ALT=\"y%5E3=y%5E5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >...divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3 ALIGN=MIDDLE  ALT=\"y%5E3\"   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=4y%5E3%2Fy%5E3=y%5E5%2Fy%5E3 ALIGN=MIDDLE  ALT=\"4y%5E3%2Fy%5E3=y%5E5%2Fy%5E3\"   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=4=y%5E2 ALIGN=MIDDLE  ALT=\"4=y%5E2\"   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=y=sqrt%284%29 ALIGN=MIDDLE  ALT=\"y=sqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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+=+y%5E3 ALIGN=MIDDLE  ALT=\"x+=+y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...........if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   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+=+2%5E3 ALIGN=MIDDLE  ALT=\"x+=+2%5E3\"   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+=+8 ALIGN=MIDDLE  ALT=\"x+=+8\"   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+=+y%5E3 ALIGN=MIDDLE  ALT=\"x+=+y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...........if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   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+=+%28-2%29%5E3 ALIGN=MIDDLE  ALT=\"x+=+%28-2%29%5E3\"   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+=+-8 ALIGN=MIDDLE  ALT=\"x+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "intersection points: <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "check if all satisfy log\r<BR>\n" );
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document.write( "since we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28y%2Cx%29+=+3 ALIGN=MIDDLE  ALT=\"log+%28y%2Cx%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%280%2C0%29+%3C%3E+3 ALIGN=MIDDLE  ALT=\"log+%280%2C0%29+%3C%3E+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-this is not solution we can use\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28y%2Cx%29+=+3 ALIGN=MIDDLE  ALT=\"log+%28y%2Cx%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28log+%282%2C8%29+=+3%29 ALIGN=MIDDLE  ALT=\"highlight%28log+%282%2C8%29+=+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" > solution we can use \r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28y%2Cx%29+=+3 ALIGN=MIDDLE  ALT=\"log+%28y%2Cx%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%282%2C-8%29+%3C%3E+3 ALIGN=MIDDLE  ALT=\"log+%282%2C-8%29+%3C%3E+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-this is not solution we can use either\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-5%2C+10%2C+-10%2C+10%2C%0D%0Acircle%288%2C2%2C.114%29%2Clocate%288%2C2%2Cp%288%2C2%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-5%2C+10%2C+-10%2C+10%2Cx%5E%281%2F3%29%2C2%5E%282%2F5%29%2Ax%5E%281%2F5%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );