document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93393>Question 93393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sorry wrong equation \r<BR>\n" );
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document.write( "log9 (1/3) = y (1/3 is NOT exponent)<BR>\n" );
document.write( "Sorry<BR>\n" );
document.write( "llo </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68116 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=68116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%289%2C%281%2F3%29%29+=+y ALIGN=MIDDLE  ALT=\"log%289%2C%281%2F3%29%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The first thing to do is to convert this logarithmic form to the exponential form using the <BR>\n" );
document.write( "rule:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2CN%29+=+x ALIGN=MIDDLE  ALT=\"log%28b%2CN%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Ex+=+N ALIGN=MIDDLE  ALT=\"b%5Ex+=+N\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that by comparing the logarithmic form of the rule to the given problem you can<BR>\n" );
document.write( "identify x as equaling y, b as equaling 9, and N as equaling <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute <BR>\n" );
document.write( "these values into the exponential form and it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5Ey+=+1%2F3 ALIGN=MIDDLE  ALT=\"9%5Ey+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can make a couple of changes. First, recognize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E-1 ALIGN=MIDDLE  ALT=\"3%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Substitute this into the equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5Ey+=+3%5E%28-1%29 ALIGN=MIDDLE  ALT=\"9%5Ey+=+3%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now notice that 9 is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2 ALIGN=MIDDLE  ALT=\"3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So replace the 9 with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2 ALIGN=MIDDLE  ALT=\"3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E2%29%5Ey+=+3%5E%28-1%29 ALIGN=MIDDLE  ALT=\"%283%5E2%29%5Ey+=+3%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "by the power rule of exponents you can multiply the exponent y by the exponent 2 to make the<BR>\n" );
document.write( "left side of the equation change as indicated:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%282y%29+=+3%5E%28-1%29 ALIGN=MIDDLE  ALT=\"3%5E%282y%29+=+3%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the bases of the two sides are both 3. Therefore, for the sides to be equal, the<BR>\n" );
document.write( "two exponents must also be equal. When you set the two exponents equal you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+-1 ALIGN=MIDDLE  ALT=\"2y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for y by dividing both sides by 2 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%29%2F2+=+-1%2F2 ALIGN=MIDDLE  ALT=\"y+=+%28-1%29%2F2+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's the answer for y. <BR>\n" );
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document.write( "Check it out by substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for y in the original problem to get ...<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%289%2C%281%2F3%29%29+=+-1%2F2 ALIGN=MIDDLE  ALT=\"log%289%2C%281%2F3%29%29+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you convert this to exponential form you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E%28-1%2F2%29+=+1%2F3 ALIGN=MIDDLE  ALT=\"9%5E%28-1%2F2%29+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But a negative exponent becomes a positive exponent if you put it (along with its base) into<BR>\n" );
document.write( "the denominator of a fraction. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"9%5E%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%289%5E%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"1%2F%289%5E%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the <BR>\n" );
document.write( "equation is then:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9%5E%281%2F2%29+=+1%2F3 ALIGN=MIDDLE  ALT=\"1%2F9%5E%281%2F2%29+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then recognize that the exponent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells you to take the square root of its base. So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"9%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > means to take the square root of 9 and the square root of 9 is 3.<BR>\n" );
document.write( "So you can <BR>\n" );
document.write( "replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"9%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 3 and the equation is finally reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+=+1%2F3 ALIGN=MIDDLE  ALT=\"+1%2F3+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since this is true, you know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-1%2F2 ALIGN=MIDDLE  ALT=\"y+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the correct answer.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how it can be worked. </SPAN>\n" );
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