document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169002>Question 169002</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132402866/algebrahomeworkh>college algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> can somebody help me solve this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28x%2B2%29=7%5E%28x-2%29 ALIGN=MIDDLE  ALT=\"5%5E%28x%2B2%29=7%5E%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124630 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=124630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help<BR>\n" );
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document.write( "can somebody help me solve this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28x%2B2%29=7%5E%28x-2%29 ALIGN=MIDDLE  ALT=\"5%5E%28x%2B2%29=7%5E%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "first we must take the log of both sides, log is the inverse function of an exponent, it is also the power of a base function<BR>\n" );
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document.write( "The two sides will have a base of \"10\"<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%2810%2C+5%5E%28x%2B2%29%29=log+%28+10%2C7%5E%28x-2%29%29 ALIGN=MIDDLE  ALT=\"log+%2810%2C+5%5E%28x%2B2%29%29=log+%28+10%2C7%5E%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%28+a%2C+b%5Ec+%29+=+%28c%29%28log%28a%2Cb%29%29+ ALIGN=MIDDLE  ALT=\"+log+%28+a%2C+b%5Ec+%29+=+%28c%29%28log%28a%2Cb%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, if there is an exponent in a log such as (x+2), and (x-2), you take the exponents and multiply them by ( <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%2810%2C+base%29+ ALIGN=MIDDLE  ALT=\"+log+%2810%2C+base%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >), in this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%28+10%2C5%29 ALIGN=MIDDLE  ALT=\"+log+%28+10%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%2810%2C7%29+ ALIGN=MIDDLE  ALT=\"+log+%2810%2C7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29log+%2810%2C5%29=%28x-2%29log+%28+10%2C7%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29log+%2810%2C5%29=%28x-2%29log+%28+10%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
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document.write( "We can rearrange the two sides<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29log+%2810%2C5%29=%28x-2%29log+%28+10%2C7%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29log+%2810%2C5%29=%28x-2%29log+%28+10%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%2810%2C5%29%28x%2B2%29=log+%28+10%2C7%29%28x-2%29 ALIGN=MIDDLE  ALT=\"log+%2810%2C5%29%28x%2B2%29=log+%28+10%2C7%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "we can use the distribution to multiply the numbers out<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%2810%2C5%29%28x%2B2%29=log+%28+10%2C7%29%28x-2%29 ALIGN=MIDDLE  ALT=\"log+%2810%2C5%29%28x%2B2%29=log+%28+10%2C7%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28log+%2810%2C5%29%29%28highlight%28x%29%2B2%29=highlight%28log+%28+10%2C7%29%29%28highlight%28x%29-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28log+%2810%2C5%29%29%28x%2Bhighlight%282%29%29=highlight%28log+%28+10%2C7%29%29%28x-highlight%282%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Remember the signs<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29%29+%2B+2log+%2810%2C5%29+=+x%28log+%28+10%2C7%29%29+-+2log+%28+10%2C7%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
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document.write( " now we need to get all the \"x\"s on one side, we will move <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C7%29%29+ ALIGN=MIDDLE  ALT=\"+x%28log+%28+10%2C7%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29%29+%2B+2log+%2810%2C5%29+=+x%28log+%28+10%2C7%29%29+-+2log+%28+10%2C7%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29%29+%2B+2log+%2810%2C5%29+-+x%28log+%28+10%2C7%29%29+=+x%28log+%28+10%2C7%29%29+-+x%28log+%28+10%2C7%29%29+-+2log+%28+10%2C7%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29%29+%2B+2log+%2810%2C5%29+-+x%28log+%28+10%2C7%29%29+=+-+2log+%28+10%2C7%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we will move <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2log+%2810%2C5%29+ ALIGN=MIDDLE  ALT=\"+2log+%2810%2C5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29%29+%2B+2log+%2810%2C5%29+-+x%28log+%28+10%2C7%29%29+=+-+2log+%28+10%2C7%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29%29+%2B+2log+%2810%2C5%29+-+2log+%2810%2C5%29+-+x%28log+%28+10%2C7%29%29+=+-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29%29+-+x%28log+%28+10%2C7%29%29+=+-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can take out the \"x\"s on the left side ( since they both have it in common<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29%29+-+x%28log+%28+10%2C7%29%29+=+-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+=+-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29+ ALIGN=MIDDLE  ALT=\"+x%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+=+-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To find \"x\" you would divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%28+10%2C5+%29+-+log+%28+10%2C7%29+ ALIGN=MIDDLE  ALT=\"+log+%28+10%2C5+%29+-+log+%28+10%2C7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+=+-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29+ ALIGN=MIDDLE  ALT=\"+x%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+=+-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29%29%2F%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+=+%28-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29%29%2F%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%28cross%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29%29%29%2Fcross%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+=+%28-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29%29%2F%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29%29%2F%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-+2log+%28+10%2C7%29+-+2log+%2810%2C5%29%29%2F%28log+%28+10%2C5+%29+-+log+%28+10%2C7%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+21.13308+ ALIGN=MIDDLE  ALT=\"+x+=+21.13308+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)(you have to solve using a calculator)<BR>\n" );
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document.write( "You usually check by replacing \"x\" with the answer, but in this case, it would be hard since the answer never stops ( I checked it, and it is right )<BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
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