document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112248>Question 112248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation:\r<BR>\n" );
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document.write( "3^0.16x=1.5\r<BR>\n" );
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document.write( "i've tried to take logs of both sides but it doesn't come out with the right answer.\r<BR>\n" );
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document.write( "Thanks in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81897 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=81897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to solve:<BR>\n" );
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document.write( "3^0.16x=1.5<BR>\n" );
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document.write( "If this is exactly the way the problem was presented to you, then by the rules of algebra this<BR>\n" );
document.write( "problem is to be interpreted as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E0.16x=1.5 ALIGN=MIDDLE  ALT=\"3%5E0.16x=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E0.16 ALIGN=MIDDLE  ALT=\"3%5E0.16\"   DISABLED_style= \"max-width:90%; height:auto;\" > is just a calculator problem.  It equals 1.192173326 and substituting<BR>\n" );
document.write( "this into the equation reduces it to ...<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.192173326%2Ax+=+1.5 ALIGN=MIDDLE  ALT=\"1.192173326%2Ax+=+1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then just divide both sides of the equation by 1.192173326 and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.5%2F1.102173326+=+1.258206308 ALIGN=MIDDLE  ALT=\"x+=+1.5%2F1.102173326+=+1.258206308\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "However, if you meant the equation to be:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%280.16%2Ax%29+=+1.5 ALIGN=MIDDLE  ALT=\"3%5E%280.16%2Ax%29+=+1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then it is a whole different problem. In this case, you could solve it by taking the log<BR>\n" );
document.write( "(assume base 10) of both sides and you would have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C3%5E%280.16%2Ax%29%29+=+log%2810%2C1.5%29 ALIGN=MIDDLE  ALT=\"log%2810%2C3%5E%280.16%2Ax%29%29+=+log%2810%2C1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Bring the exponent out as a multiplier and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.16%2Ax%2Alog%2810%2C3%29+=+log%2810%2C+1.5%29 ALIGN=MIDDLE  ALT=\"0.16%2Ax%2Alog%2810%2C3%29+=+log%2810%2C+1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A calculator tells you that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C3%29+=+0.477121254 ALIGN=MIDDLE  ALT=\"log%2810%2C3%29+=+0.477121254\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C1.5%29+=+0.176091259 ALIGN=MIDDLE  ALT=\"log%2810%2C1.5%29+=+0.176091259\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Substitute these values into the equation and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.16%2Ax%2A%280.477121254%29+=+0.176091259 ALIGN=MIDDLE  ALT=\"0.16%2Ax%2A%280.477121254%29+=+0.176091259\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side the 0.16 times 0.477121254 gives 0.0763394 ... substitute this value for<BR>\n" );
document.write( "that product and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0763394%2Ax+=+0.176091259 ALIGN=MIDDLE  ALT=\"0.0763394%2Ax+=+0.176091259\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 0.0763394 and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.176091259%2F0.0763394+=+2.30668904 ALIGN=MIDDLE  ALT=\"x+=+0.176091259%2F0.0763394+=+2.30668904\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps to lead you to the correct answer.<BR>\n" );
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