document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238613>Question 238613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am struggling to solve this problem:\r<BR>\n" );
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document.write( "  3 to the square root of 12x  + 3         3 to the square root of 3x       <BR>\n" );
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document.write( "                4\r<BR>\n" );
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document.write( "Sorry I don't know how to formally write it out on the computer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175311 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=175311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [3 (raised to the power of the radical 12x) +3 ] all divided by 4 is equal to 3 (raised to the power of the radical 3x), <BR>\n" );
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document.write( "[3^(sqrt(12x)) + 3]/4 = 3^(sqrt(3x))<BR>\n" );
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document.write( "Multiply both sides by 4; Also simplify sqrt(12x) = 2sqrt(3x)<BR>\n" );
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document.write( "[3^[2sqrt(3x)]+3] = 4*3^(sqrt(3x))<BR>\n" );
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document.write( "[3^sqrt(3x)]^2 + 3 = 4*3^(sqrt(3x))<BR>\n" );
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document.write( "This is a quadratic where the variable is 3^(sqrt(3x))<BR>\n" );
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document.write( "Let m = 3^(sqrt(3x))<BR>\n" );
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document.write( "Substitute to get the following quadratic:<BR>\n" );
document.write( "m^2 - 4m + 3 = 0<BR>\n" );
document.write( "Factor and solve for \"m\":<BR>\n" );
document.write( "(m-3)(m-1) = 0<BR>\n" );
document.write( "m = 3 or m = 1<BR>\n" );
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document.write( "Convert back to \"x\":<BR>\n" );
document.write( "3^(sqrt(3x))= 3<BR>\n" );
document.write( "sqrt(3x) = 1<BR>\n" );
document.write( "3x = 1<BR>\n" );
document.write( "x = 1/3<BR>\n" );
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document.write( "OR<BR>\n" );
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document.write( "3^(sqrt(3x)) = 1<BR>\n" );
document.write( "sqrt(3x) must be 0<BR>\n" );
document.write( "3x = 0<BR>\n" );
document.write( "x = 0<BR>\n" );
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document.write( "Final answer: x = 1/3 or x = 0<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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