document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92951>Question 92951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I will try to write this correctly -\r<BR>\n" );
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document.write( "5^x-1 = 125^2x+3  ( the x-1 and 2x+3 should all be in superscript and raised)<BR>\n" );
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document.write( "need to solve\r<BR>\n" );
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document.write( "thank<BR>\n" );
document.write( "lucy<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 #67643 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=67643\">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=5%5E%28x-1%29+=+125%5E%282x%2B3%29 ALIGN=MIDDLE  ALT=\"5%5E%28x-1%29+=+125%5E%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28x-1%29+=+%285%5E3%29%5E%282x%2B3%29 ALIGN=MIDDLE  ALT=\"5%5E%28x-1%29+=+%285%5E3%29%5E%282x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 125 as <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28x-1%29+=+5%5E%283%282x%2B3%29%29 ALIGN=MIDDLE  ALT=\"5%5E%28x-1%29+=+5%5E%283%282x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28x-1%29+=+5%5E%286x%2B9%29 ALIGN=MIDDLE  ALT=\"5%5E%28x-1%29+=+5%5E%286x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "Now that we have the same base, we can set the exponents equal to each other\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=6x%2B9 ALIGN=MIDDLE  ALT=\"x-1=6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6x%2B9%2B1 ALIGN=MIDDLE  ALT=\"x=6x%2B9%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6x=9%2B1 ALIGN=MIDDLE  ALT=\"x-6x=9%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 6x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+x=9%2B1 ALIGN=MIDDLE  ALT=\"-5+x=9%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+x ALIGN=MIDDLE  ALT=\"1+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+x ALIGN=MIDDLE  ALT=\"-6+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left side to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+x ALIGN=MIDDLE  ALT=\"-5+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+x=10 ALIGN=MIDDLE  ALT=\"-5+x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms 1 and 9 on the right side to get 10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2810%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"x=%2810%29%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide both sides by  -5 to isolate and solve for x\r<BR>\n" );
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document.write( "<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;\" > Reduce\r<BR>\n" );
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document.write( "So our answer is\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "----------------------------------\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-2-1%29+=+125%5E%282%28-2%29%2B3%29 ALIGN=MIDDLE  ALT=\"5%5E%28-2-1%29+=+125%5E%282%28-2%29%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" > into the original equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-2-1%29+=+125%5E%28-4%2B3%29 ALIGN=MIDDLE  ALT=\"5%5E%28-2-1%29+=+125%5E%28-4%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-3%29+=+125%5E%28-1%29 ALIGN=MIDDLE  ALT=\"5%5E%28-3%29+=+125%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5%5E3+=+1%2F125 ALIGN=MIDDLE  ALT=\"1%2F5%5E3+=+1%2F125\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5E%28-1%29 ALIGN=MIDDLE  ALT=\"125%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F125%5E1 ALIGN=MIDDLE  ALT=\"1%2F125%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is just  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F125 ALIGN=MIDDLE  ALT=\"1%2F125\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28-3%29 ALIGN=MIDDLE  ALT=\"5%5E%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5%5E3 ALIGN=MIDDLE  ALT=\"1%2F5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F125+=+1%2F125 ALIGN=MIDDLE  ALT=\"1%2F125+=+1%2F125\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5%5E3 ALIGN=MIDDLE  ALT=\"1%2F5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F125 ALIGN=MIDDLE  ALT=\"1%2F125\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since the equations are equal, our answer is verified. </SPAN>\n" );
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