document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91335>Question 91335</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help Solve this problem:\r<BR>\n" );
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document.write( "2^4x = 8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66666 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=66666\">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=2%5E%284x%29+=+8 ALIGN=MIDDLE  ALT=\"2%5E%284x%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To find x take the logarithm of both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C2%5E%284x%29%29+=+log%2810%2C8%29 ALIGN=MIDDLE  ALT=\"log%2810%2C2%5E%284x%29%29+=+log%2810%2C8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By the rule for exponents in logarithms, the exponent \"4x\" can be brought out as the multiplier<BR>\n" );
document.write( "of the logarithm on the left side. This converts the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2Alog%2810%2C2%29+=+log%2810%2C8%29 ALIGN=MIDDLE  ALT=\"4x%2Alog%2810%2C2%29+=+log%2810%2C8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can use a calculator to find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C2%29+=+0.301029995 ALIGN=MIDDLE  ALT=\"log%2810%2C2%29+=+0.301029995\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C8%29+=+0.903089987 ALIGN=MIDDLE  ALT=\"log%2810%2C8%29+=+0.903089987\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute these into the equation and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2A%280.301029995%29+=+0.903089987 ALIGN=MIDDLE  ALT=\"4x%2A%280.301029995%29+=+0.903089987\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side multiply the 4 times 0.301029995 to get 1.204119983. This becomes the<BR>\n" );
document.write( "multiplier of x so the equation is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.204119983x+=+0.903089987 ALIGN=MIDDLE  ALT=\"1.204119983x+=+0.903089987\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for x by dividing both sides by 1.204119983:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.903089987%2F1.204119983+=+0.75 ALIGN=MIDDLE  ALT=\"x+=+0.903089987%2F1.204119983+=+0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So x is equal to 0.75 or its fraction equivalent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "There is an easier way to do the problem.  Notice that you were given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%284x%29+=+8 ALIGN=MIDDLE  ALT=\"2%5E%284x%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then notice that 8 equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3 ALIGN=MIDDLE  ALT=\"2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If you substitute this for 8 the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%284x%29+=+2%5E3 ALIGN=MIDDLE  ALT=\"2%5E%284x%29+=+2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "For this to be true, the exponent of 2 on the left side must equal the exponent of 2 on<BR>\n" );
document.write( "the right side.  Therefore, 4x must equal 3, and when you divide both sides by 4 (the multiplier<BR>\n" );
document.write( "of x), the equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F4 ALIGN=MIDDLE  ALT=\"x+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. That was quicker and easier. You could also<BR>\n" );
document.write( "have done it in the second step of our original solution ... the step where we took the<BR>\n" );
document.write( "logs of both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C2%5E%284x%29%29+=+log%2810%2C8%29 ALIGN=MIDDLE  ALT=\"log%2810%2C2%5E%284x%29%29+=+log%2810%2C8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "At this stage if you replace 8 by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3 ALIGN=MIDDLE  ALT=\"2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > the right side changes and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C2%5E%284x%29%29+=+log%2810%2C2%5E3%29 ALIGN=MIDDLE  ALT=\"log%2810%2C2%5E%284x%29%29+=+log%2810%2C2%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now the rule of exponents in logs applies to both left and right sides and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2Alog%2810%2C2%29+=+3%2Alog%2810%2C2%29 ALIGN=MIDDLE  ALT=\"4x%2Alog%2810%2C2%29+=+3%2Alog%2810%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C2%29 ALIGN=MIDDLE  ALT=\"log%2810%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the log terms disappear from both sides so you<BR>\n" );
document.write( "are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+3 ALIGN=MIDDLE  ALT=\"4x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and when you divide both sides of this equation by 4 the result again is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F4 ALIGN=MIDDLE  ALT=\"x+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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