document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119200>Question 1119200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log[base2](x+1)-log[base4]x=1\r<BR>\n" );
document.write( "\n" );
document.write( "note: book says to change log[base4]x to base 2.<BR>\n" );
document.write( "ANSWER IS {1}.    <BR>\n" );
document.write( "Can not figure how they arrived at the answer x 2 days!!!  I know how to change from base 4 to base 2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734670 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13206)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "log[base2] of a number x is twice log[base4] of the same number x, because 4 is 2 squared:<br><BR>\n" );
document.write( "log[base 4}x = n  -->   x = 4^n = (2^2)^n = 2^(2n)  -->  log[base2]x = 2n<br><BR>\n" );
document.write( "Your book says to change log[base4]x to an equivalent expression involving log[base2].  Since log[base4] of a number is half of log[base2] of the same number, that would introduce fractions into the calculations.<br><BR>\n" );
document.write( "I would much rather change the log[base2] expression into an equivalent expression using log[base4].<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%2B1%29%29-log%284%2Cx%29+=+1 ALIGN=MIDDLE  ALT=\"log%282%2C%28x%2B1%29%29-log%284%2Cx%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >    given equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Alog%284%2C%28x%2B1%29%29-log%284%2Cx%29+=+1 ALIGN=MIDDLE  ALT=\"2%2Alog%284%2C%28x%2B1%29%29-log%284%2Cx%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  convert log base 2 to log base 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28x%2B1%29%5E2%29-log%284%2Cx%29+=+1 ALIGN=MIDDLE  ALT=\"log%284%2C%28x%2B1%29%5E2%29-log%284%2Cx%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  n*log(x) = log(x^n)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28%28%28x%2B1%29%5E2%29%2Fx%29%29+=+1 ALIGN=MIDDLE  ALT=\"log%284%2C%28%28%28x%2B1%29%5E2%29%2Fx%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >     log(a)-log(b) = log(a/b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%5E2%29%2Fx+=+4%5E1+=+4 ALIGN=MIDDLE  ALT=\"%28%28x%2B1%29%5E2%29%2Fx+=+4%5E1+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >        definition of logarithms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1+=+4x ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+=+0\"   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 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );