document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=824581>Question 824581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the exponential equation. Express the solution set in terms of natural logarithms.\r<BR>\n" );
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document.write( "4^x+4 = 5^2x+5\r<BR>\n" );
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document.write( "Answers:\r<BR>\n" );
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document.write( "A) {7 ln 5 - 5 ln 4}<BR>\n" );
document.write( "B) {5 ln 5 - 4 ln 4/ln 4 - 2 ln 5}<BR>\n" );
document.write( "C) {ln[5^5/4^4 - 4/5^2]}<BR>\n" );
document.write( "D) {ln 5 - ln 4} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497829 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4^(x+4) = 5^(2x+5) <BR>\n" );
document.write( "take ln of each side<BR>\n" );
document.write( "ln(4^(x+4) ) = ln( 5^(2x+5) )<BR>\n" );
document.write( "(x+4)ln(4) = (2x+5)ln(5)<BR>\n" );
document.write( "ln(4)*x + 4ln(4) = ln(5)*2x + 5ln(5)<BR>\n" );
document.write( "subtract 4ln(4) from each side<BR>\n" );
document.write( "ln(4)*x = ln(5)*2x + 5ln(5)-4ln(4)<BR>\n" );
document.write( "subtract ln(5)*2x from each side<BR>\n" );
document.write( "ln(4)*x - ln(5)*2x = 5ln(5)-4ln(4)<BR>\n" );
document.write( "ln(4)*x - ln(5^2)*x = ln(5^5)-ln(4^4)<BR>\n" );
document.write( "(ln(4) - ln(5^2))*x = ln(5^5)-ln(4^4)<BR>\n" );
document.write( "divide each side by (ln(4) - ln(5^2))<BR>\n" );
document.write( " x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+ln%285%5E5%29-ln%284%5E4%29+%29%2F%28+%28ln%284%29+-+ln%285%5E2%29%29+%29 ALIGN=MIDDLE  ALT=\"%28+ln%285%5E5%29-ln%284%5E4%29+%29%2F%28+%28ln%284%29+-+ln%285%5E2%29%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This can be rewritten as<BR>\n" );
document.write( " x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+5ln%285%29-4ln%284%29+%29%2F%28+%28ln%284%29+-+2ln%285%29%29+%29 ALIGN=MIDDLE  ALT=\"%28+5ln%285%29-4ln%284%29+%29%2F%28+%28ln%284%29+-+2ln%285%29%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is the same as B) assuming <BR>\n" );
document.write( "B) (5 ln 5 - 4 ln 4)/(ln 4 - 2 ln 5) </SPAN>\n" );
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