document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=366565>Question 366565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x=2 to the power y write 2 to the power 2y and 2 to the 2y+1 in terms of x and\r<BR>\n" );
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document.write( "solve the equation 2 to the 2y+1 -5(2 to the y)+2=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #261235 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=261235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If x=2 to the power y write 2 to the power 2y and 2 to the 2y+1 in terms of x and solve the equation 2 to the 2y+1 -5(2 to the y)+2=0\r<BR>\n" );
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document.write( "x = 2^y<BR>\n" );
document.write( "2^(2y) is what in terms of x<BR>\n" );
document.write( "2^(2y + 1) is what in terms of x<BR>\n" );
document.write( "solve 2^(2y + 1) - 5(2^y) + 2 = 0\r<BR>\n" );
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document.write( "logarithmic rule: if b^y = x then logb x = y<BR>\n" );
document.write( "in this case b = 2\r<BR>\n" );
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document.write( "if x = 2^y then log2 x = y\r<BR>\n" );
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document.write( "2^(2y) = 2^(2log2 x) = 2^(log2 x^2)<BR>\n" );
document.write( "logarithmic rule: logb (m^n) = nlogb m\r<BR>\n" );
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document.write( "2^(2y + 1) = 2^(log2 x^2 + 1)<BR>\n" );
document.write( "1 = log2 (2)<BR>\n" );
document.write( "2^(2y + 1) = 2^(log2 x^2 + log2 2)<BR>\n" );
document.write( "logarithmic rule: logb m + logb n = logb mn<BR>\n" );
document.write( "2^(2y + 1) = 2^(log2 x^2 + log2 2) = 2^(log2 2x^2)\r<BR>\n" );
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document.write( "solve 2^(2y + 1) - 5(2^y) + 2 = 0<BR>\n" );
document.write( "2^(log2 2x^2) - 5x + 2 = 0<BR>\n" );
document.write( "2^(log2 2x^2) = 5x - 2<BR>\n" );
document.write( "log2 (5x - 2) = log2 (2x^2)<BR>\n" );
document.write( "if these 2 logs equal then 5x - 2 = 2x^2<BR>\n" );
document.write( "-2x^2 + 5x - 2 = 0<BR>\n" );
document.write( "2x^2 - 5x + 2 = 0<BR>\n" );
document.write( "x^2 - (5/2)x + 1 = 0<BR>\n" );
document.write( "(x - 2)(x - (1/2)) = 0, check with FOIL, First Outer Inner Last<BR>\n" );
document.write( "x^2 - (1/2)x - 2x + 1 --> x^2 - (1/2)x - (4/2)x + 1<BR>\n" );
document.write( "x^2 - (1/2)x - (4/2)x + 1 = x^2 - (5/2)x + 1, yes<BR>\n" );
document.write( "x = 2 or x = 1/2<BR>\n" );
document.write( "x = 2^y --> log2 x = y<BR>\n" );
document.write( "log2 2 = 1<BR>\n" );
document.write( "log2 (1/2) = -1\r<BR>\n" );
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document.write( " </SPAN>\n" );
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