document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126695>Question 126695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x)= 3(1/125)(^x-2)+12,then what is the value of x when f(x)=87? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92842 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=92842\">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=f%28x%29=+3%2A%281%2F125%29%5E%28x-2%29%2B12 ALIGN=MIDDLE  ALT=\"f%28x%29=+3%2A%281%2F125%29%5E%28x-2%29%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When f(x) = 87 this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=87+=+3%281%2F125%29%5E%28x-2%29%2B12 ALIGN=MIDDLE  ALT=\"87+=+3%281%2F125%29%5E%28x-2%29%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Transpose this equation (just switch sides) so the unknown x is on the left side. This transposition<BR>\n" );
document.write( "makes the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281%2F125%29%5E%28x-2%29%2B12+=+87 ALIGN=MIDDLE  ALT=\"3%281%2F125%29%5E%28x-2%29%2B12+=+87\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 12 on the left side by subtracting 12 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281%2F125%29%5E%28x-2%29+=+75 ALIGN=MIDDLE  ALT=\"3%281%2F125%29%5E%28x-2%29+=+75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next, get rid of the multiplier 3 on the left side by dividing both sides by 3 to reduce<BR>\n" );
document.write( "the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F125%29%5E%28x-2%29+=+25 ALIGN=MIDDLE  ALT=\"%281%2F125%29%5E%28x-2%29+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side of the equation, you can simplify it by applying the power rule of exponents<BR>\n" );
document.write( "to both the numerator and the denominator of the fraction to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E%28x-2%29%2F125%5E%28x-2%29+=+25 ALIGN=MIDDLE  ALT=\"1%5E%28x-2%29%2F125%5E%28x-2%29+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But for the numerator you can apply the rule that 1 raised to any power is just 1. When you<BR>\n" );
document.write( "apply that rule, the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F125%5E%28x-2%29+=+25 ALIGN=MIDDLE  ALT=\"1%2F125%5E%28x-2%29+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the denominator by multiplying both sides of this equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5E%28x-2%29 ALIGN=MIDDLE  ALT=\"125%5E%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+125%5E%28x-2%29%2A%2825%29 ALIGN=MIDDLE  ALT=\"1+=+125%5E%28x-2%29%2A%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But 125 can be replaced by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E3 ALIGN=MIDDLE  ALT=\"5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 25 can be replaced by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2 ALIGN=MIDDLE  ALT=\"5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. When you do that you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+%285%5E3%29%5E%28x-2%29%2A5%5E2 ALIGN=MIDDLE  ALT=\"1+=+%285%5E3%29%5E%28x-2%29%2A5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Apply the power rule by raising the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E3 ALIGN=MIDDLE  ALT=\"5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2 ALIGN=MIDDLE  ALT=\"x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > power to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+5%5E%283%2A%28x-2%29%29%2A5%5E2 ALIGN=MIDDLE  ALT=\"1+=+5%5E%283%2A%28x-2%29%29%2A5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply out the exponent and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+5%5E%283x-6%29%2A5%5E2 ALIGN=MIDDLE  ALT=\"1+=+5%5E%283x-6%29%2A5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you multiply two common bases that are raised to an exponent, the rule is that you <BR>\n" );
document.write( "add the exponents. So in this case you add 3x - 6 and 2 to get the exponent of 5 and the equation<BR>\n" );
document.write( "then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+5%5E%283x+-+6+%2B+2%29 ALIGN=MIDDLE  ALT=\"1+=+5%5E%283x+-+6+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify the exponent by combining the -6 and the +2 and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+5%5E%283x+-4%29 ALIGN=MIDDLE  ALT=\"1+=+5%5E%283x+-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now here's a little tricky insight. If you raise any number to the zero power the answer<BR>\n" );
document.write( "is 1. So if you raise 5 to the zero power it will equal the 1 on the left side of this equation.<BR>\n" );
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document.write( "Therefore, we can say that the exponent 3x - 4 must equal zero. In equation form, this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+-+4+=+0 ALIGN=MIDDLE  ALT=\"3x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the -4 on the left side by adding 4 to both sides of this equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+4 ALIGN=MIDDLE  ALT=\"3x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And solve for x by dividing both sides of this equation by 3 and you have the answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4%2F3 ALIGN=MIDDLE  ALT=\"x+=+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A little bit of work to get to this point. Hope this helps you to understand how to do the problem.<BR>\n" );
document.write( ". </SPAN>\n" );
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