document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205210>Question 205210</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x using logs  10^(x+3)=5E^(7-x)<BR>\n" );
document.write( "                          <BR>\n" );
document.write( "                         9^x=2e^x2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "pls help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154966 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154966\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve for x using logs\r<BR>\n" );
document.write( "\n" );
document.write( " 10^(x+3) = 5 * e^(7-x)<BR>\n" );
document.write( ";<BR>\n" );
document.write( "using the natural logs<BR>\n" );
document.write( "ln(10^(x+3)) = ln(5) + ln(e^(7-x)}<BR>\n" );
document.write( ":<BR>\n" );
document.write( "log equiv of exponents<BR>\n" );
document.write( "(x+3)ln(10) = ln(5) + (7-x)ln(e^}<BR>\n" );
document.write( ":<BR>\n" );
document.write( "find the natural logs, (nat log of e is 1)<BR>\n" );
document.write( "2.30(x+3) = 1.61 + 7 - x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2.3x + 6.9 = 8.61 - x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2.3x + x = 8.61 - 6.9<BR>\n" );
document.write( ":<BR>\n" );
document.write( "3.3x = 1.7<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.7%2F3.3 ALIGN=MIDDLE  ALT=\"1.7%2F3.3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = .5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check on a calc x=.5: <BR>\n" );
document.write( "10^3.5 = 3262<BR>\n" );
document.write( "5*e^6.5 = 3326<BR>\n" );
document.write( "Does not check out exactly on a calc because I dropped all those decimals<BR>\n" );
document.write( "you can use the method & retain the decimals and get a more exact value for x<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "9^x = 2 * e^(x^2)<BR>\n" );
document.write( "do this the same way<BR>\n" );
document.write( "x*ln(9) = ln(2) + x^2*ln(e)<BR>\n" );
document.write( "2.20x = .69 + x^2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "0 = x^2 - 2.2x + .69<BR>\n" );
document.write( "Use the quadratic formula to find x: a=1; b=-2.2 c=.69<BR>\n" );
document.write( "two solutions x~.38 and x~1.8<BR>\n" );
document.write( ":<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );