document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70330>Question 70330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x: 3^2x = 12\r<BR>\n" );
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document.write( "x = ?\r<BR>\n" );
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document.write( "Round to 2 decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50168 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=50168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I interpret your problem to be to solve for x in the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%282x%29+=+12 ALIGN=MIDDLE  ALT=\"3%5E%282x%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and I assume you know the use of logarithms and exponents.<BR>\n" );
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document.write( "By using the power rule of exponents you can re-write the equation in the form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%5E2%29%5Ex+=+12 ALIGN=MIDDLE  ALT=\"%283%5E2%29%5Ex+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+=+9 ALIGN=MIDDLE  ALT=\"3%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > so substitute 9 for <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;\" > to reduce the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5Ex+=+12 ALIGN=MIDDLE  ALT=\"9%5Ex+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Take the log of both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%289%29%5Ex+=+log%2812%29 ALIGN=MIDDLE  ALT=\"log%289%29%5Ex+=+log%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But by the rules of exponents in logarithms, the exponent becomes a multiplier of the<BR>\n" );
document.write( "log.  x is the exponent, so it becomes the multiplier of log(9) to give:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%289%29+=+log%2812%29 ALIGN=MIDDLE  ALT=\"x%2Alog%289%29+=+log%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To solve for x, divide both sides by log(9) to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+log%2812%29%2Flog%289%29 ALIGN=MIDDLE  ALT=\"x+=+log%2812%29%2Flog%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Calculator time!  log(12) = 1.079181246 and log(9) = 0.954242509.  By dividing log(12) by<BR>\n" );
document.write( "log(9) you find that x = 1.130929754. <BR>\n" );
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document.write( "That's the answer. By doubling it and raising 3 to that exponent on your calculator<BR>\n" );
document.write( "you will find that the answer is, as it should be, 12.<BR>\n" );
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document.write( "And don't forget to round the answer to two decimal places as the problem requests.<BR>\n" );
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document.write( "Hope that I interpreted the problem correctly and that the approach I used was not beyond<BR>\n" );
document.write( "where you are in your text. </SPAN>\n" );
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