document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=276828>Question 276828</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you enter logrithmic expressions into the calculator with subscripts </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201693 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=201693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Short answer: You can't (at least not directly).<br><BR>\n" );
document.write( "Pretty much any calculator that can do logarithms at all can do base 10 logarithms. And many of those can also do base e (ln) logarithms. I have never seen a calculator that can do logarithms of any other base.<br><BR>\n" );
document.write( "Since the subscripts you see are the bases of the logarithms, any logarithm with a subscript/base different from 10 or e cannot be done (directly) on a calculator.<br><BR>\n" );
document.write( "So how do we find logarithms of bases other than 10 or e? Answer: Use the change of base formula to convert the logarithm you have into an expression of base 10 (or base e) logarithms. The change of base formula for logarithms is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28x%29%29+=+log%28b%2C+%28x%29%29%2Flog%28b%2C+%28a%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28x%29%29+=+log%28b%2C+%28x%29%29%2Flog%28b%2C+%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Here's an example. The first step is using the change of base formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C+%28124%29%29+=+log%28%28124%29%29%2Flog%28%286%29%29+=+2.0934216851622351%2F0.7781512503836436+=+2.6902503647332542 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C+%28124%29%29+=+ln%28124%29%2Fln%286%29+=+4.8202815656050369%2F1.7917594692280550+=+2.6902503647332542 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note #1: See how the answer works out the same whether you use base 10 logarithms or base e (ln) logarithms. Even though the individual logarithms in the fraction are different, the quotient works out the same.<br><BR>\n" );
document.write( "Note #2: Any time you use a calculator to find a logarithm you will get a decimal approximation of the actual value. So these two answers, if you had a calculator with more decimal places may be different by a very, very small amount. (As you can see, the two answers we got here are the same to 16 decimal places.) </SPAN>\n" );
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