document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138686>Question 1138686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each equation. Show all steps and work. Round your answers to four decimal places.<BR>\n" );
document.write( "a. 6^2x=250<BR>\n" );
document.write( "b.〖log〗_3 (x-3)+〖log〗_3 (x-7)=4\r<BR>\n" );
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document.write( "Given the function    f(x)=〖log〗_2 (x-2)-1. <BR>\n" );
document.write( "	1. Graph the function<BR>\n" );
document.write( "	2. Find its domain & range<BR>\n" );
document.write( "	3. Write the equation of its asymptote<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756489 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=756489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "a. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E%282x%29=250 ALIGN=MIDDLE  ALT=\"6%5E%282x%29=250\"   DISABLED_style= \"max-width:90%; height:auto;\" >....take a log of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%5E%282x%29%29=log%28250%29 ALIGN=MIDDLE  ALT=\"log%286%5E%282x%29%29=log%28250%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=2x%2Alog%286%29=log%282%2A5%5E3%29 ALIGN=MIDDLE  ALT=\"2x%2Alog%286%29=log%282%2A5%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >............since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%29=log%282%2A3%29=log%282%29%2Blog%283%29 ALIGN=MIDDLE  ALT=\"log%286%29=log%282%2A3%29=log%282%29%2Blog%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2A5%5E3%29=log%282%29+%2B+3log%285%29 ALIGN=MIDDLE  ALT=\"log%282%2A5%5E3%29=log%282%29+%2B+3log%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28log%282%29%2Blog%283%29%29=log%282%29+%2B+3log%285%29 ALIGN=MIDDLE  ALT=\"2x%28log%282%29%2Blog%283%29%29=log%282%29+%2B+3log%285%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=%28log%282%29+%2B+3log%285%29%29%2F2%28log%282%29%2Blog%283%29%29 ALIGN=MIDDLE  ALT=\"x=%28log%282%29+%2B+3log%285%29%29%2F2%28log%282%29%2Blog%283%29%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=%280.69314718+%2B+4.8283137373%29%2F2%280.69314718%2B1.098612288668%29 ALIGN=MIDDLE  ALT=\"x=%280.69314718+%2B+4.8283137373%29%2F2%280.69314718%2B1.098612288668%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=5.5214609173%2F3.583518937336 ALIGN=MIDDLE  ALT=\"x=5.5214609173%2F3.583518937336\"   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=1.5408 ALIGN=MIDDLE  ALT=\"x=1.5408\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%28x-3%29%29%2Blog%283+%2C%28x-7%29%29=4 ALIGN=MIDDLE  ALT=\"log%283%2C+%28x-3%29%29%2Blog%283+%2C%28x-7%29%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .....convert 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%28%28x-3%29%29%2Flog%283%29%2Blog%28%28x-7%29%29%2Flog%283%29=4 ALIGN=MIDDLE  ALT=\"log%28%28x-3%29%29%2Flog%283%29%2Blog%28%28x-7%29%29%2Flog%283%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....both sides multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%29 ALIGN=MIDDLE  ALT=\"log%283%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%28x-3%29%29%2Blog%28%28x-7%29%29=4+log%283%29 ALIGN=MIDDLE  ALT=\"log%28%28x-3%29%29%2Blog%28%28x-7%29%29=4+log%283%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%28x-3%29%28x-7%29%29=+log%283%5E4%29 ALIGN=MIDDLE  ALT=\"log%28%28x-3%29%28x-7%29%29=+log%283%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......since log same, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x-7%29=+3%5E4 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x-7%29=+3%5E4\"   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%5E2-7x-3x%2B21=+81 ALIGN=MIDDLE  ALT=\"x%5E2-7x-3x%2B21=+81\"   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%5E2-10x%2B21-+81=0 ALIGN=MIDDLE  ALT=\"x%5E2-10x%2B21-+81=0\"   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%5E2-10x-+60=0 ALIGN=MIDDLE  ALT=\"x%5E2-10x-+60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"   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-%28-10%29%2B-sqrt%28%28-10%29%5E2-4%2A1%2A%28-60%29%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28-%28-10%29%2B-sqrt%28%28-10%29%5E2-4%2A1%2A%28-60%29%29%29%2F%282%2A1%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=%2810%2B-sqrt%28100%2B240%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2810%2B-sqrt%28100%2B240%29%29%2F2\"   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=%2810%2B-sqrt%28340%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2810%2B-sqrt%28340%29%29%2F2\"   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=%2810%2B-18.4391%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2810%2B-18.4391%29%2F2\"   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=%285%2B-9.2195%29 ALIGN=MIDDLE  ALT=\"x=%285%2B-9.2195%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=x=5%2B9.2195 ALIGN=MIDDLE  ALT=\"x=5%2B9.2195\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=14.2195 ALIGN=MIDDLE  ALT=\"x=14.2195\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5-9.2195 ALIGN=MIDDLE  ALT=\"x=5-9.2195\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-4.2195 ALIGN=MIDDLE  ALT=\"x=+-4.2195\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> since log disregard negative solution\r<BR>\n" );
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document.write( "so, your solution is:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=14.2195 ALIGN=MIDDLE  ALT=\"x=14.2195\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Given the function  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+log%282%2C+%28x-2%29%29-1+ ALIGN=MIDDLE  ALT=\"f%28x%29=+log%282%2C+%28x-2%29%29-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1. Graph the function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+log%282%2C+%28x-2%29%29-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+log%282%2C+%28x-2%29%29-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. Find its domain & range\r<BR>\n" );
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document.write( "domain: { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E2 ALIGN=MIDDLE  ALT=\"x%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "range: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > (all real numbers)\r<BR>\n" );
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document.write( "3. Write the equation of its asymptote\r<BR>\n" );
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document.write( "Vertical asymptote: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=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=log%28x+-+2%29%2Flog%282%29+-+1 ALIGN=MIDDLE  ALT=\"log%28x+-+2%29%2Flog%282%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%3E2 ALIGN=MIDDLE  ALT=\"x-%3E2\"   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=drawing+%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Aline%282%2C-10%2C2%2C10%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+log%282%2C+%28x-2%29%29-1%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Horizontal asymptote: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=none+ ALIGN=MIDDLE  ALT=\"none+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );