document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209259>Question 209259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Make x the subject of this formula:\r<BR>\n" );
document.write( "\n" );
document.write( "a = b^x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158185 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=158185\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b%5Ex ALIGN=MIDDLE  ALT=\"a+=+b%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Ca%29+=+x ALIGN=MIDDLE  ALT=\"log%28b%2Ca%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+2%5E3 ALIGN=MIDDLE  ALT=\"8+=+2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C8%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2C8%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C8%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2C8%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > using your calculator by converting the base to 10 which the calculator can handle.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the formula for doing that is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%29+=+log%28c%2Cx%29%2Flog%28c%2Cb%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29+=+log%28c%2Cx%29%2Flog%28c%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "in this particular case, we have x = 8 and b = 2 and c = 10 and the formula becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C8%29+=+log%2810%2C8%29%2Flog%2810%2C2%29 ALIGN=MIDDLE  ALT=\"log%282%2C8%29+=+log%2810%2C8%29%2Flog%2810%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "using your calculator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C8%29+=+.903089987 ALIGN=MIDDLE  ALT=\"log%2810%2C8%29+=+.903089987\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C2%29+=+.301029996 ALIGN=MIDDLE  ALT=\"log%2810%2C2%29+=+.301029996\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C8%29+=+log%2810%2C8%29%2Flog%2810%2C2%29 ALIGN=MIDDLE  ALT=\"log%282%2C8%29+=+log%2810%2C8%29%2Flog%2810%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C8%29+=+.903089987+%2F+.301029996 ALIGN=MIDDLE  ALT=\"log%282%2C8%29+=+.903089987+%2F+.301029996\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C8%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2C8%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since you already know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3 ALIGN=MIDDLE  ALT=\"2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8<BR>\n" );
document.write( "then:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C8%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2C8%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+2%5E3 ALIGN=MIDDLE  ALT=\"8+=+2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is confirmed to be a true statement.<BR>\n" );
document.write( "and:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+2%5E3 ALIGN=MIDDLE  ALT=\"8+=+2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C8%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2C8%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is also confirmed to be a true statement.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can start from either one and derive the other.<BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );