document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164541>Question 1164541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your friend claims you can use the change  -  of  -  base to write the <BR>\n" );
document.write( "expression (In x) as a common logarithm. Is your friend correct? <BR>\n" );
document.write( "Explain your reasoning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788946 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=788946\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> yes, he is correct.\r<BR>\n" );
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document.write( "y = ln(x) is the same as y = loge(x)/log(e).\r<BR>\n" );
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document.write( "take x = 1525<BR>\n" );
document.write( "ln(1525) = 7.329749689<BR>\n" );
document.write( "log(1525) / log(e) = the same.\r<BR>\n" );
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document.write( "the derivation of the log base conversion is as follows:\r<BR>\n" );
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document.write( "y = ln(x) if and only if e^y = x<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(e^y) = log(x)<BR>\n" );
document.write( "since log(e^y) = y * log(e), you get:<BR>\n" );
document.write( "y * log(e) = log(x)<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = log(x) / log(e)<BR>\n" );
document.write( "since they're both equal to y, you get:<BR>\n" );
document.write( "ln(x) = log(x) / ln(x)\r<BR>\n" );
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document.write( "that's the base conversion formula that says loga(x) = logb(x) / logb(a)\r<BR>\n" );
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document.write( "this is useful to convert all different bases to base 10.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "2^5 = 32<BR>\n" );
document.write( "this is true if and only if log2(32) = 5<BR>\n" );
document.write( "log function of your calculator gets you log to the base of 10, i.e. log10.<BR>\n" );
document.write( "you use your calculator log function to get:<BR>\n" );
document.write( "log2(32) = log(32)/log(2).<BR>\n" );
document.write( "log(32)/log(2) = 5\r<BR>\n" );
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document.write( " </SPAN>\n" );
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