document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=556154>Question 556154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would like to know if I did the first three correct and I need help on #4:<BR>\n" );
document.write( "Solve these equations:<BR>\n" );
document.write( "(a) 2x^-3=16<BR>\n" );
document.write( "1/x^3=8<BR>\n" );
document.write( "1=8x^3<BR>\n" );
document.write( "1/8=x^3<BR>\n" );
document.write( "x=1/2\r<BR>\n" );
document.write( "\n" );
document.write( "(b)2x^-3=0<BR>\n" );
document.write( "x^-3=0<BR>\n" );
document.write( "1/x^3=0 <BR>\n" );
document.write( "x=0\r<BR>\n" );
document.write( "\n" );
document.write( "(c) 2^-3x=16<BR>\n" );
document.write( "-3x=4<BR>\n" );
document.write( "x=-4/3\r<BR>\n" );
document.write( "\n" );
document.write( "(d) cuberoot 5=25^2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362070 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -----<BR>\n" );
document.write( "(a) is good.<BR>\n" );
document.write( "to confirm, use your calculator to get:<BR>\n" );
document.write( "2*(1/2)^-3 = 16<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "(b) doesn't look good.<BR>\n" );
document.write( "i don't think you have a solution for that problem.<BR>\n" );
document.write( "you start with:<BR>\n" );
document.write( "2x^(-3) = 0<BR>\n" );
document.write( "this is equivalent to:<BR>\n" );
document.write( "2/(x^(3) = 0<BR>\n" );
document.write( "multiply both sides of this equation by x^3 to get:<BR>\n" );
document.write( "2 = 0 which is not true.<BR>\n" );
document.write( "if you said that x = 0, you would not get a solution.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "2*x^(-3) = 0 becomes:<BR>\n" );
document.write( "2*0^(-3) = 0 becomes:<BR>\n" );
document.write( "2/0^3) = 0 becomes:<BR>\n" );
document.write( "undefined because you can't divide by 0.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "(c) 2^(-3x) = 16<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "1/(2^3x) = 16<BR>\n" );
document.write( "divide both sides of this equation by 16 and multiply both sides of this equation by 2^3x to get:<BR>\n" );
document.write( "2^3x = 1/16<BR>\n" );
document.write( "take the log of both sides of this equation to get:<BR>\n" );
document.write( "log(2^3x) = log(1/16)<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "3x*log(2) = log(1/16)<BR>\n" );
document.write( "divide both sides of this equation by 3*log(2) to get:<BR>\n" );
document.write( "x = log(1/16)/(3*log(2)) which becomes:<BR>\n" );
document.write( "x = -1.33333<BR>\n" );
document.write( "confirm by replacing x in your original equation:<BR>\n" );
document.write( "2^(-3x) = 16 becomes:<BR>\n" );
document.write( "2^(-3*-1.33333333) = 16 which becomes:<BR>\n" );
document.write( "2^(4) = 16 which becomes:<BR>\n" );
document.write( "16 = 16<BR>\n" );
document.write( "this confirms the value of x = -1.33333333 is good.<BR>\n" );
document.write( "note that 1.333333333 is really 1+1/3 = 4/3.<BR>\n" );
document.write( "2^(-3x) = 16 becomes:<BR>\n" );
document.write( "2^(-3*(-4/3) which becomes:<BR>\n" );
document.write( "2^4 = 16 which becomes:<BR>\n" );
document.write( "16 = 16<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "(d)<BR>\n" );
document.write( "cube root (5)=25^2x becomes:<BR>\n" );
document.write( "5^(1/3) = 25^2x<BR>\n" );
document.write( "take the log of both sides to get:<BR>\n" );
document.write( "log(5^(1/3)() = log(25^2x)<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "(1/3)*log(5) = 2*x*log(25)<BR>\n" );
document.write( "divide both sides of this equation by 2*log(25) to get:<BR>\n" );
document.write( "x = (1/3)*log(5) / (2*log(25) which becomes:<BR>\n" );
document.write( "x = log(5) / (3*2*log(25))<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = .08333333333<BR>\n" );
document.write( "confirm by substituting in original equation.<BR>\n" );
document.write( "5^(1/3) = 25^(2x) becomes:<BR>\n" );
document.write( "1.709975947 = 25^(2*.0833333333) which becomes:<BR>\n" );
document.write( "1.709975947 = 1.709975947<BR>\n" );
document.write( "this confirms the value for x is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );