document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=598192>Question 598192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve.<BR>\n" );
document.write( "4^x=(1/square root of 2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378523 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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/cgi-bin/show-face.mpl?user=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"4%5Ex=1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply the right hand side of the equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear the radical expression in the denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=%281%2Fsqrt%282%29%29%2A%28sqrt%282%29%2Fsqrt%282%29%29 ALIGN=MIDDLE  ALT=\"4%5Ex=%281%2Fsqrt%282%29%29%2A%28sqrt%282%29%2Fsqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"4%5Ex=sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Rewrite each term in the equation in terms of base 2 using exponent rules. 4=2^2, sqrt(2)=2^(1/2), and 2=2^1.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"4%5Ex=sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you raise an exponential expression to a power, you multiply the exponents, so (2^2)^x=2^2x.<BR>\n" );
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document.write( "When you divide exponential expressions, you subtract the exponents, so 2^(1/2)/2^1=2^(1/2-1)=2^(-1/2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E2%29%5Ex=2%5E%281%2F2%29%2F2%5E1%29 ALIGN=MIDDLE  ALT=\"%282%5E2%29%5Ex=2%5E%281%2F2%29%2F2%5E1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%282x%29=2%5E%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"2%5E%282x%29=2%5E%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We have 2 raised to a power on both sides of the equation. Since both expressions are equal, the exponents  must be the same, So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-1%2F2 ALIGN=MIDDLE  ALT=\"2x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F4 ALIGN=MIDDLE  ALT=\"x=-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You definitely want to check your work on these sorts of problems. Use the original equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"4%5Ex=1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%28-1%2F4%29=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"4%5E%28-1%2F4%29=1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4%5E%281%2F4%29=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2F4%5E%281%2F4%29=1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "4^(1/4) means the fourth root of 4. The fourth root of 4 is the square root of 2 since (sqrt(2))(sqrt(2))(sqrt(2))(sqrt(2))=4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%282%29=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%282%29=1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's it. x is -1/4. <BR>\n" );
document.write( "You can also solve this using logarithms. Feel free to email if you'd like to see that solution.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com<BR>\n" );
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