document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241969>Question 241969</A>: <I><SPAN STYLE=\"word-break: break-all;\"> e^x=10 Help I am so lost.. what would the approximate value be for x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177143 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=177143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> e^x = 10\r<BR>\n" );
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document.write( "this is an exponential problem.\r<BR>\n" );
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document.write( "you need logarithms to solve it.\r<BR>\n" );
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document.write( "you can use the log function of your calculator or you can use the ln function of your calculator.\r<BR>\n" );
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document.write( "the base e is the scientific constant of 2.718281828.....\r<BR>\n" );
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document.write( "This is an irrational number which means it is not the result of a division of two integers.\r<BR>\n" );
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document.write( "the fractional part is endless and non repeating.\r<BR>\n" );
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document.write( "the ln function of your calculator is the natural log function which is the inverse of the exponential function using the base of e.\r<BR>\n" );
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document.write( "exponential functions have the unknown value as the exponent.\r<BR>\n" );
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document.write( "10^x is an exponential function<BR>\n" );
document.write( "2^x is an exponential function<BR>\n" );
document.write( "3^x is an exponential function<BR>\n" );
document.write( "e^x is an exponential function\r<BR>\n" );
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document.write( "if the problem was 10^x = 10, you could probably solve this easily enough since 10^1 = 10\r<BR>\n" );
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document.write( "you would then say x = 1 and the problem would be solved.\r<BR>\n" );
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document.write( "if the problem was 10^x = 100, you could probably solve this easily enough since 10^2 = 10*10 = 100\r<BR>\n" );
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document.write( "if the problem was 10^x = 50, you might have a little more difficulty solving this.\r<BR>\n" );
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document.write( "that's where logs come in.\r<BR>\n" );
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document.write( "by definition, 10^2 = 100 if and only if log(100) = 2\r<BR>\n" );
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document.write( "they are inverse processes.  you use exponents to get there and you use logarithms to get back.\r<BR>\n" );
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document.write( "if the question was:\r<BR>\n" );
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document.write( "10^x = 100\r<BR>\n" );
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document.write( "you could solve it by logarithms.\r<BR>\n" );
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document.write( "you would take log of both sides of the equation to get:\r<BR>\n" );
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document.write( "log(10^x) = log(100)\r<BR>\n" );
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document.write( "by the laws of logarithms, log(10^x) = x * log(10)\r<BR>\n" );
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document.write( "you do need to know the laws of logarithms to help you solve these types of problems.\r<BR>\n" );
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document.write( "your equation of log(10^x) = log(100) becomes:\r<BR>\n" );
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document.write( "x*log(10) = log(100)\r<BR>\n" );
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document.write( "you divide both sides of this equation by log(10) to get:\r<BR>\n" );
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document.write( "x = log(100)/log(10) and you get:\r<BR>\n" );
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document.write( "x = 2 after you find the log of 100 and the log of 10 in your calculator.\r<BR>\n" );
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document.write( "you confirm your answer is correct by taking your original equation of:\r<BR>\n" );
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document.write( "10^x = 100\r<BR>\n" );
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document.write( "and replacing x with 2 to get:\r<BR>\n" );
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document.write( "10^2 = 100\r<BR>\n" );
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document.write( "which is correct so you solved the problem correctly.\r<BR>\n" );
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document.write( "your original problem is:\r<BR>\n" );
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document.write( "e^x = 10\r<BR>\n" );
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document.write( "you would solve this the same way.\r<BR>\n" );
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document.write( "take the log of both sides of the equation to get:\r<BR>\n" );
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document.write( "log(e^x) = log(10)\r<BR>\n" );
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document.write( "use the laws of logarithms to get:\r<BR>\n" );
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document.write( "x * log(e) = log(10)\r<BR>\n" );
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document.write( "divide both sides of this eqution by log(e) to get:\r<BR>\n" );
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document.write( "x = log(10)/log(e)\r<BR>\n" );
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document.write( "use your calculator to find log(10) and log(e) and solve for x to get:\r<BR>\n" );
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document.write( "x = 2.302585093\r<BR>\n" );
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document.write( "replace x with that in your original equation of:\r<BR>\n" );
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document.write( "e^x = 10 to get:\r<BR>\n" );
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document.write( "e^(2.302585093) = 10 which becomes:\r<BR>\n" );
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document.write( "10 = 10 confirming your answer is correct.\r<BR>\n" );
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document.write( "if you can't get e on your calculator, then use the approximation of 2.718281828 for it.\r<BR>\n" );
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document.write( "you'll get close but not right on.\r<BR>\n" );
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document.write( "2.718281828^(2.302585093) = 9.99999999996 which is very close but not right on.\r<BR>\n" );
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document.write( "if you want to find the value of e on your calculator, you need to follow the instructions of your calculator.\r<BR>\n" );
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document.write( "my calculator is a TI-30XA (maybe $12.00 or so).\r<BR>\n" );
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document.write( "to display the value of e i would do the following:\r<BR>\n" );
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document.write( "enter 1<BR>\n" );
document.write( "enter 2d ln\r<BR>\n" );
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document.write( "that displays e^1 which is the value of e\r<BR>\n" );
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document.write( "if i want to store that, i enter:<BR>\n" );
document.write( "sto 1\r<BR>\n" );
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document.write( "the value of e is stored in memory location number 1\r<BR>\n" );
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document.write( "i can then use the value of e not rounded whenever i need it.\r<BR>\n" );
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document.write( "you need to review basic exponents and basic logarithms if you're having great difficulty with this.\r<BR>\n" );
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document.write( "try this website.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/solvexpo.htm\" target = \"_blank\">Purple Math</a>\r<BR>\n" );
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document.write( "try this one also.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut45_expeq.htm\" target = \"_blank\">WTAMU</a>\r<BR>\n" );
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document.write( "try some lessons from <a  rel=nofollow HREF= \"http://www.algebra.com/tutors/all-lessons.mpl\" target = \"_blank\">Algebra.Com Lessons</a>\r<BR>\n" );
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document.write( "Search for the ones you need.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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