document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012454>Question 1012454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good evening, I have some difficulties with this logarithmic equation:<BR>\n" );
document.write( "4log4((x+1)^(1/2)) - log2(5-7x)=0<BR>\n" );
document.write( "I tried to solve changing the base in such a way:<BR>\n" );
document.write( "4log4((x+1)^(1/2)) = (log4(5-7x))/log4(2)<BR>\n" );
document.write( "but I do wrong somewhere solving the arguments.<BR>\n" );
document.write( "Can somebody help me explaining the right method?<BR>\n" );
document.write( "Many thanks  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628391 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=628391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you were on the right track.  log 4 (2)=1/2, and dividing by 1/2 is multiplying by 2, which is what I did when I converted to base 2, rather than base 4.\r<BR>\n" );
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document.write( "4log4((x+1)^(1/2)) =log2(5-7x)<BR>\n" );
document.write( "log 4 (x+1)^2=log 2 (5-7x)<BR>\n" );
document.write( "log2 (x+1)^2/log2 (4)=log 2 (5-7x)<BR>\n" );
document.write( "log2(4)=2, multiply by 2 both sides<BR>\n" );
document.write( "log 2(x+1)^2=log 2 (5-7x)^2<BR>\n" );
document.write( "(x+1)^2=(5-7x)^2<BR>\n" );
document.write( "x^2+2x+1=25-70x+49x^2<BR>\n" );
document.write( "0=24-72x+48x^2<BR>\n" );
document.write( "divide both sides by 24<BR>\n" );
document.write( "2x^2-3x+1=0<BR>\n" );
document.write( "(2x-1)(x-1)=0<BR>\n" );
document.write( "x=1/2, 1<BR>\n" );
document.write( "check back<BR>\n" );
document.write( "4 log 4(2^(1/2)-log 2 (5-7)=0; the second term does not exist.<BR>\n" );
document.write( "4 log 4 (3/2)^(1/2)-log2 (5-3.5)=0<BR>\n" );
document.write( "log 4 (3/2)^2=log 2 (3/2)<BR>\n" );
document.write( "log 2 (3/2)^2/log 2 (4)=log 2 (3/2)<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "The second term is 0.585 or 2^0.585=1.5<BR>\n" );
document.write( "the first term is 4 log 4(3/2)^(1/2)<BR>\n" );
document.write( "3/2^(1/2)=1.225<BR>\n" );
document.write( "4 log 4 (1.225), and log 4(1.225)=0.1465<BR>\n" );
document.write( "0.1465*4=0.586, rounding error.<BR>\n" );
document.write( "log 2 (4)=2<BR>\n" );
document.write( "multiply through by 2<BR>\n" );
document.write( "log 2 (3/2)^2=2 log 2 (3/2)=log 2 (3/2)^2<BR>\n" );
document.write( "x=1/2\r<BR>\n" );
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