document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=267671>Question 267671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this equation:\r<BR>\n" );
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document.write( " log(base a) 5 = -3/4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196698 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=196698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%285%29%29+=+-3%2F4 ALIGN=MIDDLE  ALT=\"log%28a%2C+%285%29%29+=+-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Eventually we want an equation that says<BR>\n" );
document.write( "a = some-number<BR>\n" );
document.write( "So we need to get the \"a\" out of the base of the logarithm. We can so this by rewriting the equation in exponential form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+=+a%5E%28-3%2F4%29 ALIGN=MIDDLE  ALT=\"5+=+a%5E%28-3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we need to change the exponent on \"a\" to a 1 (because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E1+=+a ALIGN=MIDDLE  ALT=\"a%5E1+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >). The quickest way to do this make clever use of the rules for exponents. I am going to raise both sides of the equation to the -4/3 power. (See what happens to see why.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%5E%28-4%2F3%29+=+%28a%5E%28-3%2F4%29%29%5E%28-4%2F3%29 ALIGN=MIDDLE  ALT=\"%285%29%5E%28-4%2F3%29+=+%28a%5E%28-3%2F4%29%29%5E%28-4%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On the right side, the rule is to multiply the exponents. And what do you get when you multiply -3/4 and -4/3? Answer: 1!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-4%2F3%29+=+a ALIGN=MIDDLE  ALT=\"5%5E%28-4%2F3%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This may be an acceptable answer. If you want a decimal approximation you can use your calculator on the expression on the left side. Or, for an exact answer with rational denominators...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-4%2F3%29+=+a ALIGN=MIDDLE  ALT=\"5%5E%28-4%2F3%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5%5E%284%2F3%29+=+a ALIGN=MIDDLE  ALT=\"1%2F5%5E%284%2F3%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Froot%283%2C+5%5E4%29+=+a ALIGN=MIDDLE  ALT=\"1%2Froot%283%2C+5%5E4%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Froot%283%2C+5%5E4%29%29%28root%283%2C+5%5E2%29%2Froot%283%2C+5%5E2%29%29+=+a ALIGN=MIDDLE  ALT=\"%281%2Froot%283%2C+5%5E4%29%29%28root%283%2C+5%5E2%29%2Froot%283%2C+5%5E2%29%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+5%5E2%29%2Froot%283%2C+5%5E6%29+=+a ALIGN=MIDDLE  ALT=\"root%283%2C+5%5E2%29%2Froot%283%2C+5%5E6%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+5%5E2%29%2F5%5E2+=+a ALIGN=MIDDLE  ALT=\"root%283%2C+5%5E2%29%2F5%5E2+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+25%29%2F25+=+a ALIGN=MIDDLE  ALT=\"root%283%2C+25%29%2F25+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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