document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119247>Question 119247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x \r<BR>\n" );
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document.write( "log10 (5-x) = 3 log10  2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87349 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=87349\">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=log%2810%2C%285-x%29%29=3%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%285-x%29%29=3%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the right side you can take the multiplier 3 to the inside of the log operator if you <BR>\n" );
document.write( "make it an exponent. This makes the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%285-x%29%29=log%2810%2C%282%5E3%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%285-x%29%29=log%2810%2C%282%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Continuing on the right side, cube the 2 to get 8, making the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%285-x%29%29=+log%2810%2C%288%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%285-x%29%29=+log%2810%2C%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that both sides have an operator of log to the base 10. For both sides of this equation<BR>\n" );
document.write( "to be equal, the quantities that the log operator is applied to must be equal. This means<BR>\n" );
document.write( "that <BR>\n" );
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document.write( "5 - x must equal 8. In equation form this is:<BR>\n" );
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document.write( "5 - x = 8<BR>\n" );
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document.write( "Get rid of the 5 on the left side by subtracting 5 from both sides to get:<BR>\n" );
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document.write( "-x = 3<BR>\n" );
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document.write( "Solve for x by multiplying both sides of this equation by -1 and the result is:<BR>\n" );
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document.write( "x = -3<BR>\n" );
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document.write( "That's the answer. You can check it by substituting -3 for x in the original equation you<BR>\n" );
document.write( "were given. Start with the original equation of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%285-x%29%29=3%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%285-x%29%29=3%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute -3 for x and this equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%285-%28-3%29%29%29=3%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%285-%28-3%29%29%29=3%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify the left side by recognizing that 5 - (-3) = 5 + 3 = 8. This makes the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%288%29%29=3%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%288%29%29=3%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Using a calculator you can determine that the base 10 log of 8 is 0.903089987 and the<BR>\n" );
document.write( "base 10 log of 2 is 0.301029995. Substituting these values results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.903089987+=+3+%2A+0.301029995 ALIGN=MIDDLE  ALT=\"0.903089987+=+3+%2A+0.301029995\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you multiply out the right side you will see that this equation is true, and therefore the<BR>\n" );
document.write( "answer of x = -3 is correct.<BR>\n" );
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document.write( "Hope this helps you to work your way through this problem.<BR>\n" );
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