document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189490>Question 1189490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) write log(x^3 √(x+1)/(x-2)^2, x>2 as a sum and difference logarithms.Express all powers as factors.\r<BR>\n" );
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document.write( "b) Find the exact value of the composite function cos[sin^-1(-1/3)]\r<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 #820866 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=820866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%5E3+%2Asqrt%28%28x%2B1%29%29%2F%28x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"log%28x%5E3+%2Asqrt%28%28x%2B1%29%29%2F%28x-2%29%5E2%29\"   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;\" > as a sum and difference logarithms.<BR>\n" );
document.write( "Express all powers as factors.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%5E3%2A+sqrt%28%28x%2B1%29%29%2F%28x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"log%28x%5E3%2A+sqrt%28%28x%2B1%29%29%2F%28x-2%29%5E2%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%5E3%29%2Blog%28+sqrt%28%28x%2B1%29%29%2F%28x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"log%28x%5E3%29%2Blog%28+sqrt%28%28x%2B1%29%29%2F%28x-2%29%5E2%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=3log%28x%29%2Blog%28+sqrt%28x%2B1%29%29-log%28%28x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"3log%28x%29%2Blog%28+sqrt%28x%2B1%29%29-log%28%28x-2%29%5E2%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=3log%28x%29%2Blog%28%28x%2B1%29%5E%281%2F2%29%29-2log%28%28x-2%29%29 ALIGN=MIDDLE  ALT=\"3log%28x%29%2Blog%28%28x%2B1%29%5E%281%2F2%29%29-2log%28%28x-2%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=3log%28x%29%2B%281%2F2%29log%28%28x%2B1%29%29-2log%28%28x-2%29%29 ALIGN=MIDDLE  ALT=\"3log%28x%29%2B%281%2F2%29log%28%28x%2B1%29%29-2log%28%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "True for all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Verify solution <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;\" >:  The solution is <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( "b) Find the exact value of the composite function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28sin%5E-1%28-1%2F3%29%29 ALIGN=MIDDLE  ALT=\"cos%28sin%5E-1%28-1%2F3%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=cos%28sin%5E-1%28-1%2F3%29%29 ALIGN=MIDDLE  ALT=\"cos%28sin%5E-1%28-1%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E-1%28-1%2F3%29=theta ALIGN=MIDDLE  ALT=\"sin%5E-1%28-1%2F3%29=theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=-1%2F3 ALIGN=MIDDLE  ALT=\"sin%28theta%29=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that we are now looking for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Next, use the identity : \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1\"   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=cos%28theta%29=sqrt%281-sin%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29=sqrt%281-sin%5E2%28theta%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=cos%28theta%29=sqrt%281-%28-1%2F3%29%5E2%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29=sqrt%281-%28-1%2F3%29%5E2%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=cos%28theta%29=sqrt%288%2F9%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29=sqrt%288%2F9%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=cos%28theta%29=%282sqrt%282%29%29%2F3 ALIGN=MIDDLE  ALT=\"cos%28theta%29=%282sqrt%282%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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