document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005734>Question 1005734</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5. Solve the following equations\r<BR>\n" );
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document.write( "a) 3^m=81\r<BR>\n" );
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document.write( "b) (36p^4)12=24\r<BR>\n" );
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document.write( "c) 5^n×5^n+4=25\r<BR>\n" );
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document.write( "d) 4^7x/256=64^2x+2/16^2x&#8722;1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621895 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3^m=81<BR>\n" );
document.write( "m=4.  One can take logs, but 3^2=9 and 9^2=81.<BR>\n" );
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document.write( "(36p^4)12=24 <BR>\n" );
document.write( "36p^4=2<BR>\n" );
document.write( "18p^4=1<BR>\n" );
document.write( "18p^4-1=0<BR>\n" );
document.write( "This can be p^4=(1/18)<BR>\n" );
document.write( "p= +/- (1/18)^(1/4).  That is two roots.  You get the other complex ones by setting it up this way:<BR>\n" );
document.write( "(sqrt(18)p^2+1)(sqrt(18) p^2-1)=0<BR>\n" );
document.write( "the second is p^2=(1/sqrt(18) p=+/ - 1/18^(1/4)<BR>\n" );
document.write( "The first is p= i +/- 1/18^(1/4)<BR>\n" );
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document.write( "5^n×5^n+4=25 <BR>\n" );
document.write( "5^(2n+4)=25=5^2<BR>\n" );
document.write( "Therefore, 2n+4=2, since the bases are equal. If we took logs to base 5, the base would disappear.<BR>\n" );
document.write( "2n+4=2<BR>\n" );
document.write( "n= -1<BR>\n" );
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document.write( "4^7x/256=64^2x+2/16^2x&#8722;1<BR>\n" );
document.write( "4^7x/4^4=4^(7x-4).  That is the left side.<BR>\n" );
document.write( "4^3(2x+2)/4^2(2x-1). That is the right side.<BR>\n" );
document.write( "4^(7x-4)=4^(6x+6)/4^(4x-2)<BR>\n" );
document.write( "log to base 4<BR>\n" );
document.write( "7x-4= log 4  4^(6x+6-4x+2)=2x+8<BR>\n" );
document.write( "5x=12<BR>\n" );
document.write( "x=12/5<BR>\n" );
document.write( "This checks.  <BR>\n" );
document.write( "The left side will be 50859008.46, which is 4^(84/5)-(20/5) or 4^(64/5)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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