document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202363>Question 202363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if (125/27)^x = the cubic root of 0.6 then the value of x is _______\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 #152589 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=152589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your original equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28125%2F27%29%5Ex+=+%28.6%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28125%2F27%29%5Ex+=+%28.6%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "by the laws of logarithms, this can only be true if and only if<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28125%2F27%29%2C%28%28.6%29%5E%281%2F3%29%29%29+=+x+ ALIGN=MIDDLE  ALT=\"log%28%28125%2F27%29%2C%28%28.6%29%5E%281%2F3%29%29%29+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we can convert this log with a base of (125/27) to a log with a base of 10 so that we can solve it using the calculator.<BR>\n" );
document.write( "the logarithm base conversion formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28125%2F27%29%2C%28%28.6%29%5E%281%2F3%29%29%29+=+log%2810%2C%28%28.6%29%5E%281%2F3%29%29%29+%2F+log%2810%2C%28125%2F27%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "our formula now becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%2810%2C%28%28.6%29%5E%281%2F3%29%29%29+%2F+log%2810%2C%28125%2F27%29%29+ ALIGN=MIDDLE  ALT=\"+log%2810%2C%28%28.6%29%5E%281%2F3%29%29%29+%2F+log%2810%2C%28125%2F27%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "now:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28%28.6%29%5E%281%2F3%29%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28%28.6%29%5E%281%2F3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2A%28log%2810%2C%28.6%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29%2A%28log%2810%2C%28.6%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "also:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%2810%2C%28125%2F27%29%29+ ALIGN=MIDDLE  ALT=\"+log%2810%2C%28125%2F27%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%2810%2C125%29+-+log%2810%2C27%29+ ALIGN=MIDDLE  ALT=\"+log%2810%2C125%29+-+log%2810%2C27%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so the equation becomes:<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F3%29%2A%28log%2810%2C%28.6%29%29%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2F3%29%2A%28log%2810%2C%28.6%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > / <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28log%2810%2C125%29+-+log%2810%2C27%29%29+ ALIGN=MIDDLE  ALT=\"+%28log%2810%2C125%29+-+log%2810%2C27%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you can now use your calculator to solve this.<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F3%29%2A%28-.22184875%29%29%2F%28%282.096910013%29-%281.431363764%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2F3%29%2A%28-.22184875%29%29%2F%28%282.096910013%29-%281.431363764%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-0.073949583%29%2F%28.665546249%29 ALIGN=MIDDLE  ALT=\"%28-0.073949583%29%2F%28.665546249%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "x = -0.1111111111111<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove your answer is correct, substitute it in the original equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28125%2F27%29%5E%28-0.111111111111%29+=+%28.6%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28125%2F27%29%5E%28-0.111111111111%29+=+%28.6%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.843432665+=+.843432665 ALIGN=MIDDLE  ALT=\"0.843432665+=+.843432665\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is true.<BR>\n" );
document.write( "note that .843432665 = (.6)^(1/3)<BR>\n" );
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