document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148022>Question 148022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need some help on these problems.\r<BR>\n" );
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document.write( "1.  y varies directly as x and inversely as the square root of w; write the sentence as an equation.\r<BR>\n" );
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document.write( "2.  write 3^x=y in log form.\r<BR>\n" );
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document.write( "3.  write log 2^x=y in exponential form.\r<BR>\n" );
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document.write( "4.  solve for x; 5x/6-x/3=1/6\r<BR>\n" );
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document.write( "thanks for the help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108407 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=108407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "When \"y varies directly as x\", this means that as x increases y increases. Also as x decreases y decreases. So the first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=kx ALIGN=MIDDLE  ALT=\"y=kx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If let k be any number and you plug in values of x (say 1,2,3, etc), you'll notice that y will increase along with x.\r<BR>\n" );
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document.write( "Furthermore, when varies inversely as the square root of w, this means that as the square root of w increases y decreases. Also as square root of w decreases y increases. So the second equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=k%2Fsqrt%28w%29 ALIGN=MIDDLE  ALT=\"y=k%2Fsqrt%28w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "Now if you combine the two equations, you get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28kx%29%2F%28sqrt%28w%29%29 ALIGN=MIDDLE  ALT=\"y=%28kx%29%2F%28sqrt%28w%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the entire sentence \"y varies directly as x and inversely as the square root of w\" translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28kx%29%2F%28sqrt%28w%29%29 ALIGN=MIDDLE  ALT=\"y=%28kx%29%2F%28sqrt%28w%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ex=y ALIGN=MIDDLE  ALT=\"3%5Ex=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%28y%29%29=x ALIGN=MIDDLE  ALT=\"log%283%2C%28y%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the equation using the property: <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;\" > ===> <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;\" > \r<BR>\n" );
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document.write( "So the equation in logarithmic form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%28y%29%29=x ALIGN=MIDDLE  ALT=\"log%283%2C%28y%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%282%5Ex%29%29=y ALIGN=MIDDLE  ALT=\"log%2810%2C%282%5Ex%29%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5Ey=2%5Ex ALIGN=MIDDLE  ALT=\"10%5Ey=2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the equation using the property: <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;\" > ====> <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 the equation in exponential form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5Ey=2%5Ex ALIGN=MIDDLE  ALT=\"10%5Ey=2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "# 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2F6-x%2F3=1%2F6 ALIGN=MIDDLE  ALT=\"5x%2F6-x%2F3=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%285x%2Fcross%286%29-x%2Fcross%283%29%29=cross%286%29%281%2Fcross%286%29%29 ALIGN=MIDDLE  ALT=\"6%285x%2Fcross%286%29-x%2Fcross%283%29%29=cross%286%29%281%2Fcross%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear any fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-2x=1 ALIGN=MIDDLE  ALT=\"5x-2x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=1 ALIGN=MIDDLE  ALT=\"3x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%29%2F%283%29 ALIGN=MIDDLE  ALT=\"x=%281%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <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( "Answer:\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.333 ALIGN=MIDDLE  ALT=\"x=0.333\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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