document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=549482>Question 549482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to help my niece with an equation. Solving with logarithms, the equation is 5^x=4^(x+3). I cannot remember for the life of me how to solve this..Can you help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357784 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=357784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am trying to help my niece with an equation. Solving with logarithms, the equation is 5^x=4^(x+3). I cannot remember for the life of me how to solve this.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "using the exponent rule for logs:<BR>\n" );
document.write( "xlog5=(x+3)log4<BR>\n" );
document.write( "x/(x+3)=log4/log5<BR>\n" );
document.write( "using calculator<BR>\n" );
document.write( "x/(x+3)&#8776;.8614<BR>\n" );
document.write( "x=.8614x+3*.8614<BR>\n" );
document.write( "x-.8614x=2.5841<BR>\n" );
document.write( ".1386x=2.5814<BR>\n" );
document.write( "x=2.5814/.1386=18.6185<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "5^x=5^18.6185=1.0322*10^13<BR>\n" );
document.write( "4^(x+3)=4^(21.6185)=1.0366*10^13<BR>\n" );
document.write( "difference due to rounding errors </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );