document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103116>Question 1103116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have this exponential equation that I cannot seem to solve:\r<BR>\n" );
document.write( "\n" );
document.write( "5^x = 4^x+1\r<BR>\n" );
document.write( "\n" );
document.write( "I didn't get very far; here's my lame attempt:\r<BR>\n" );
document.write( "\n" );
document.write( "log5^x = log4^x+1<BR>\n" );
document.write( "xlog5 = (x+1) log4\r<BR>\n" );
document.write( "\n" );
document.write( "and that's about it.  I don't know if I should distribute the log4 over the (x+1) or what.  I know the answer is log4/log5/4  (\"log 4 divided by log 5/4\"), but I don't know how to get there.  Can you help?<BR>\n" );
document.write( "Thank you\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717793 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(Note that the given equation, as you show it, is 5^x = 4^x + 1, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5Ex+=+4%5Ex%2B1 ALIGN=MIDDLE  ALT=\"5%5Ex+=+4%5Ex%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >; that is much different than the equation you are really trying to solve, which is 5^x = 4^(x+1), or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5Ex+=+4%5E%28x%2B1%29 ALIGN=MIDDLE  ALT=\"5%5Ex+=+4%5E%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  As another tutor on this site likes to say, \"parentheses are free -- use them!\")<br><BR>\n" );
document.write( "You have done all you can do with the logarithms; now you have an equation in just x which you can solve.<br><BR>\n" );
document.write( "Yes; distribute.   Then solve for x (hint gather all the terms with x on one side of the equation).<br><BR>\n" );
document.write( "Then note that the given answer, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%29%2Flog%285%2F4%29 ALIGN=MIDDLE  ALT=\"log%284%29%2Flog%285%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, can be written, using laws of logarithms, as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%29%2F%28log%285%29-log%284%29%29 ALIGN=MIDDLE  ALT=\"log%284%29%2F%28log%285%29-log%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "When you finish solving your equation for x, that is exactly what you should get. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );