document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28486>Question 28486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log(3x)= 2.7logx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15479 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log(3x) = 2.7 logx<BR>\n" );
document.write( "log (3x) = log3 + logx<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "this is easy to prove<BR>\n" );
document.write( "say you're using logs to the base 10<BR>\n" );
document.write( "log(10 * 10 * 10) = log 1000 = 3<BR>\n" );
document.write( "but also<BR>\n" );
document.write( "log10 + log10 + log10 = 3<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "log3 + logx = 2.7 logx<BR>\n" );
document.write( "subtract logx from both sides<BR>\n" );
document.write( "log3 = 2.7 logx - logx<BR>\n" );
document.write( "log3 = 1.7 logx<BR>\n" );
document.write( "log3 = logx^1.7<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "I know this last step is true because <BR>\n" );
document.write( "3log(1000) = 3 * 3 = 9<BR>\n" );
document.write( "and <BR>\n" );
document.write( "log(1000)^3 = log(1000 * 1000 * 1000) = log(1000000000) = 9<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "3 = x^1.7<BR>\n" );
document.write( "raise each side to the 1/1.7 power<BR>\n" );
document.write( "3^(1/1.7) = x^(1.7/1.7)<BR>\n" );
document.write( "because x^1 = x<BR>\n" );
document.write( "3^(1/1.7) = x  answer </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );