document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=474483>Question 474483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a scientific calculator the base for a lagarithm equation is 10 by default. How to change the base? Please explain elaborately. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325411 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=325411\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the base change formula is very simple.<BR>\n" );
document.write( "the formula 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+%2F+log%28c%2Cb%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29+=+log%28c%2Cx%29+%2F+log%28c%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b is equal to the base you are converting from.<BR>\n" );
document.write( "c is equal to the base you are converting to.<BR>\n" );
document.write( "you are taking the log of x to the base of c and you are dividing that by the log of b to the base of c.<BR>\n" );
document.write( "the bases you are converting to are most often the base of 10 or the base of e.<BR>\n" );
document.write( "the base of 10 is the LOG function of your calculator.<BR>\n" );
document.write( "the base of e is the LN function of your calculator.<BR>\n" );
document.write( "If you have a logarithm that is other than to the base of 10 or the base of e, then you can solve it using your calculator by converting to the base of 10 or to the base of e.<BR>\n" );
document.write( "note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2Cx%29 ALIGN=MIDDLE  ALT=\"log%2810%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is shown as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%29 ALIGN=MIDDLE  ALT=\"log%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "note also that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2Cx%29 ALIGN=MIDDLE  ALT=\"log%28e%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is shown as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29 ALIGN=MIDDLE  ALT=\"ln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "to convert from any base to the base of 10, the formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%29+=+log%28x%29+%2F+log%2810%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29+=+log%28x%29+%2F+log%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to convert from any base to the base of e, the formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%29+=+ln%28x%29+%2F+ln%2810%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29+=+ln%28x%29+%2F+ln%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "an example will clarify:<BR>\n" );
document.write( "suppose you have a number such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C64%29 ALIGN=MIDDLE  ALT=\"log%282%2C64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C64%29 ALIGN=MIDDLE  ALT=\"log%282%2C64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6 because you know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ey ALIGN=MIDDLE  ALT=\"2%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 64.<BR>\n" );
document.write( "if you didn't know that, you would use the conversion formula to get it to the base of 10 so you can use the log function of your calculator, or you would usse the conversion formula to get it to the base of e so you can use the ln function of your calculator.<BR>\n" );
document.write( "the conversion formulas are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C64%29+=+log%2864%29%2Flog%282%29+=+6 ALIGN=MIDDLE  ALT=\"log%282%2C64%29+=+log%2864%29%2Flog%282%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C64%29+=+ln%2864%29%2Fln%282%29+=+6 ALIGN=MIDDLE  ALT=\"log%282%2C64%29+=+ln%2864%29%2Fln%282%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "note that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C64%29+=+log%2864%29%2Flog%282%29+=+6 ALIGN=MIDDLE  ALT=\"log%282%2C64%29+=+log%2864%29%2Flog%282%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C64%29+=+log%2810%2C64%29%2Flog%2810%2C2%29+=+6 ALIGN=MIDDLE  ALT=\"log%282%2C64%29+=+log%2810%2C64%29%2Flog%2810%2C2%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "note also that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C64%29+=+ln%2864%29%2Fln%282%29+=+6 ALIGN=MIDDLE  ALT=\"log%282%2C64%29+=+ln%2864%29%2Fln%282%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C64%29+=+log%28e%2C64%29%2Flog%28e%2C2%29+=+6 ALIGN=MIDDLE  ALT=\"log%282%2C64%29+=+log%28e%2C64%29%2Flog%28e%2C2%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a very short version of what I just said can be found here:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://hyperphysics.phy-astr.gsu.edu/hbase/logm.html\" target = \"_blank\">http://hyperphysics.phy-astr.gsu.edu/hbase/logm.html</a> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );