document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=383402>Question 383402</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to solve \r<BR>\n" );
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document.write( "3*log7(base 3) without using calculator?\r<BR>\n" );
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document.write( "note : 3*log7(base 3) = log7^3(base 3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #271537 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=271537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm guessing you posted this yesterday and I \"solved\" it for you. But I misread the problem and solved something else. Sorry about that!<br><BR>\n" );
document.write( "If your problem is to find the number for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Alog%283%2C+%287%29%29 ALIGN=MIDDLE  ALT=\"3%2Alog%283%2C+%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%287%5E3%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C+%287%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%28343%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C+%28343%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >), without a calculator, then the answer is: <i>It can't be done!</i> (This leads me to suspect that problem may actually be the problem I thought it was yesterday.)<br><BR>\n" );
document.write( "7 is not a well-known power of 3, 3 is not a well-known power of 7 and both numbers, 3 and 7, are not well-known powers of some other number. One of these would have to be true in order to answer this question without a calculator.<br><BR>\n" );
document.write( "If the 7 was a 9 instead then we could solve this problem because 9 is a well-known power of 3. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+3%5E2 ALIGN=MIDDLE  ALT=\"9+=+3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%289%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%283%2C+%289%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Alog%283%2C+%289%29%29+=+3%2A2+=+6 ALIGN=MIDDLE  ALT=\"3%2Alog%283%2C+%289%29%29+=+3%2A2+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The only thing you can do with your expression is to convert it to an expression of logarithms of a different base. For example, if you did want to use your calculator to find a decimal approximation for the value of your expression, then we could use the base conversion formula for logarithms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to convert your base 3 logarithm into a base that your calculator \"knows\" like base 10 or base e (aka ln). Converting your base 3 logarithm into base e logarithms we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%287%29%29+=+ln%287%29%2Fln%283%29 ALIGN=MIDDLE  ALT=\"log%283%2C+%287%29%29+=+ln%287%29%2Fln%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which would make your full expression:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Alog%283%2C+%287%29%29+=+3%2A%28ln%287%29%2Fln%283%29%29 ALIGN=MIDDLE  ALT=\"3%2Alog%283%2C+%287%29%29+=+3%2A%28ln%287%29%2Fln%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With this we could then use our calculator to obtain a decimal approximation for the value of your expression. </SPAN>\n" );
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