document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133315>Question 1133315</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi need help on this question\r<BR>\n" );
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document.write( "The variables x and y are connected by the equation y= ax^n where a and n are constants. Given that y=6360 when x = 10, find the values of a and n to 3 s.f\r<BR>\n" );
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document.write( "this is what I have done lg y = lg a + nlg x <BR>\n" );
document.write( "                                       Lg 6360 = lg a +nlg 10<BR>\n" );
document.write( "Don't know what to do next.  Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750535 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=750535\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> unless i'm missing something, it appears that a and n can be anything.<BR>\n" );
document.write( "if you pick an a, you can solve for n.<BR>\n" );
document.write( "if you pick an n, you can solve for a.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "your equation is y = a * x^n\r<BR>\n" );
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document.write( "you are given that y = 6360 when x = 10.\r<BR>\n" );
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document.write( "your equation becomes 6360 = a * 10^n\r<BR>\n" );
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document.write( "you can pick any positive value for a and solve for n.\r<BR>\n" );
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document.write( "you can pick any positive or negative value for n and solve for a.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "let a = 5.\r<BR>\n" );
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document.write( "the equation becomes 6360 = 5 * 10^n<BR>\n" );
document.write( "divide both sides by 5 to get 6360/5 = 10^n<BR>\n" );
document.write( "take log of both sides to get log(6360/5) = log(10^n)<BR>\n" );
document.write( "this becomes log(6360/5) = n * log(10)<BR>\n" );
document.write( "solve for n to get n = log(6360/5)/log(10) = 3.104407111\r<BR>\n" );
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document.write( "your equation becomes 6360 = 5 * 10^3.104407111<BR>\n" );
document.write( "evaluate to get 6360 = 6360\r<BR>\n" );
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document.write( "a can't be negative because they you'll be taking the log of a negative number which is not allowed.\r<BR>\n" );
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document.write( "allow n to be equal -5.\r<BR>\n" );
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document.write( "the equation becomes 6360 = a * 10^-5<BR>\n" );
document.write( "divide by 10^-5 to get 6360 / 10^-5 = a<BR>\n" );
document.write( "solve for a to get a = 636000000\r<BR>\n" );
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document.write( "equation becomes 6360 = 636000000 * 10^-5<BR>\n" );
document.write( "evaluate to get 6360 = 6360\r<BR>\n" );
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document.write( "there are an infinite number of values of a and n that will satisfy this equation as long as a is not negative.\r<BR>\n" );
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document.write( "the problem in getting a unique solution is that you have one equation in 2 unknowns.\r<BR>\n" );
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document.write( "in order to get a unique solution, you need to have the same number of unknowns as the number of equations.\r<BR>\n" );
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document.write( "i built a table in excel with various values of n given to show you that there is no limit to the possible values of a from that.\r<BR>\n" );
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document.write( "i chose values of n from -10 to +10.\r<BR>\n" );
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document.write( "the values of a were calculated, and then the values of a and n were used to solve the equation of y = a*10^n\r<BR>\n" );
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document.write( "the value of n can be anything and you will get a value of a that makes the equation true.\r<BR>\n" );
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document.write( "that's my thinking.\r<BR>\n" );
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document.write( "perhaps the questions was not posed correctly?\r<BR>\n" );
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document.write( "when given the value of n, i didn't even need logs.\r<BR>\n" );
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document.write( "if given a when a is positive, i used logs to solve for n.\r<BR>\n" );
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document.write( "here's the results of excel.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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