document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72121>Question 72121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, please could you give me a hand on these questions? I have tried hard but i can't find my way with proofs:\r<BR>\n" );
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document.write( "3i)Prove that log of m (in the base a) - log of n (in the base a) = log of (m over n)( in the base a).\r<BR>\n" );
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document.write( "4i)Prove that nlog of x (in the base m) = log of x to the power of n (in the base m).\r<BR>\n" );
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document.write( "5a)Prove that log of b (in the base a) = log of b( in the base 10) over log of a (in the base 10).\r<BR>\n" );
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document.write( "Thank you very much for your help!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51548 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=51548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let log(base a)m = X ; let log(base a)n= Y<BR>\n" );
document.write( "Then a^(X)=m and a^Y=n<BR>\n" );
document.write( "Then m/n = a^X/a^Y = a^(X-Y)<BR>\n" );
document.write( "Take the log(base a) of both sides to get:<BR>\n" );
document.write( "log(base a)(m/n) = log(base a)a^(X-Y)<BR>\n" );
document.write( "log(base a)(m/n) = X-y<BR>\n" );
document.write( "log(base a)(x/n) = log(base a)m - log(base a)n<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "The proof for log(base a)mn = log(base a)m + log(base a)n <BR>\n" );
document.write( "is almost identical:<BR>\n" );
document.write( "You get a line that says:<BR>\n" );
document.write( "mn=a^X * a^Y = a^(X+Y)<BR>\n" );
document.write( "Take the log(base a) of both sides to get:<BR>\n" );
document.write( "log(base a)mn = log(base a)a^(X+Y)<BR>\n" );
document.write( "log(base a)mn = X+Y<BR>\n" );
document.write( "log(base a)mn = log(base a)m + log(base a)n<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( " log(base a)m^n = ?<BR>\n" );
document.write( "Let log(base a)m = X<BR>\n" );
document.write( "Then a^X = m<BR>\n" );
document.write( "Substitute for \"m\" to get:<BR>\n" );
document.write( "log(base a)(a^X)^n = log(base a)a^(Xn)= Xn<BR>\n" );
document.write( "Substitute for X to get:<BR>\n" );
document.write( "=nlog(base a)m<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Log(base a)b = x<BR>\n" );
document.write( "Let a^x = b <BR>\n" );
document.write( "Then x log(base 10) a = log(base 10 b<BR>\n" );
document.write( "And x= [log(base 10)b] / [log(base 10)a]<BR>\n" );
document.write( "Substitute for \"x\" to get<BR>\n" );
document.write( "log(base a)b = log(base 10)b /log(base 10)a<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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