zeralda21 Posted April 3, 2011 Share Posted April 3, 2011 (edited) Would like some help with an equation. f(x)=e^2x g(x)=lnx The equation is: f(g(x))=g(f(x^3)). f(g(x))=e^2lnx and g(f(x^3))=ln(e^(2x^3) e^2lnx=ln(e^(2x^3) I´m stuck now. I don´t know how to continue to simplify further than this. Would like a hint or a tip so I can proceed. Edited April 3, 2011 by zeralda21 Link to comment Share on other sites More sharing options...
insane_alien Posted April 3, 2011 Share Posted April 3, 2011 i'd probably move the e^2 into the Ln(x) and then get rid of the ln's and go from there. whether its the right approach or not, well, i suppose you'll find out. Link to comment Share on other sites More sharing options...
CaptainBlood Posted April 3, 2011 Share Posted April 3, 2011 Try to do e^(e^2lnx) = e^(ln(e^(2x^3)) then you should get e^2 = 2x^3 and solve for x Link to comment Share on other sites More sharing options...
zeralda21 Posted April 3, 2011 Author Share Posted April 3, 2011 Thanks. I´ll try to work from here. I´ll be back with the result. Link to comment Share on other sites More sharing options...
` melody. Posted April 4, 2011 Share Posted April 4, 2011 e2lnx = elnx^2 And given that e and ln are opposite functions, elnx^2 cancel out to just = x2 So you probably would simplify it down to x2 = 2 x3 and then solve for x. I'm not 100% sure though. Hope it helps. Link to comment Share on other sites More sharing options...
Hal. Posted April 4, 2011 Share Posted April 4, 2011 (edited) More to follow .... Edited April 5, 2011 by hal_2011 Link to comment Share on other sites More sharing options...
zeralda21 Posted April 6, 2011 Author Share Posted April 6, 2011 e2lnx = elnx^2 And given that e and ln are opposite functions, elnx^2 cancel out to just = x2 So you probably would simplify it down to x2 = 2 x3 and then solve for x. I'm not 100% sure though. Hope it helps. Yes, you are right, I couldn´t figure out e^2lnx at first. x^2=2x^3 is the simplified equation. x^2-2x^3=0 x=0 or 1/2. But since ln is not defined for x=0, the answer is x=1/2. Anyway, thanks! Link to comment Share on other sites More sharing options...
Hal. Posted April 6, 2011 Share Posted April 6, 2011 (edited) A solution has been found , the original poster is happy and I need the practice ! I didn't finish with a quadratic so ....... interesting ! Let me know if there is a mistake . Edited April 6, 2011 by hal_2011 Link to comment Share on other sites More sharing options...
zeralda21 Posted April 7, 2011 Author Share Posted April 7, 2011 A solution has been found , the original poster is happy and I need the practice ! I didn't finish with a quadratic so ....... interesting ! Let me know if there is a mistake . This is really good, different altough a correct answer. Thanks. Link to comment Share on other sites More sharing options...
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