document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238822>Question 238822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to prove why the following equations are equal to each other.  I have tried factoring, and using the rules for logarithms (meaning using multiplication when adding and division when subtracting).  I still can not figure it out.  I do not know how to use subscripts for math problems on a computer so if you don't understand what I am asking it is completely understandable.  But for now I will use log(2) of 3, meaning a log with a base of two, of three.  Here is the equation:<BR>\n" );
document.write( "[6log(2)3] / [1 + log(2)3] = [6ln3] / [ln2 + ln3]<BR>\n" );
document.write( "Thank you, <BR>\n" );
document.write( "Heather </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175470 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=175470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [6log(2)3] / [1 + log(2)3] = [6ln3] / [ln2 + ln3]<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Working with the left side:<BR>\n" );
document.write( "6[ln(3)/ln(2)] / [1 + ln(3)/ln(2)]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= [6ln(3)]/[ln(2)] divided by [ln(2) + ln(3)]/[ln(2)]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "If you invert the denominator and multiply the ln(2)'s cancel <BR>\n" );
document.write( "and you end up with:<BR>\n" );
document.write( "= [6ln(3)] divided by [ln(2) + ln(3)]<BR>\n" );
document.write( "which is the right side you your original equation.<BR>\n" );
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document.write( "Comment: The key here is that you see that log(2)3 = ln(3)/ln(2)<BR>\n" );
document.write( "That is using the Change of base Rule.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );