Thursday, 2 July 2015

algebra precalculus - Find x when the function equals 0




I must solve for x for this function.



ex20x=0



I'm not sure what to do here. I've tried this so far but it makes no sense:
ex=20xxlne=ln20+lnxxln20=lnx



I tried this as well but I'm not sure if this is right either:
ex=20xlnex=ln20xx=ln20+lnx



I've got more confidence in the second try, although I don't know how to solve for an actual number.




The answer is a decimal.


Answer



This equation cannot be solved in terms of elementary functions. You can either use numeric methods like Newton's, or solve in terms of Lambert W function:



ex20x=020x=exxex=120xex=120x=W(120)x=W(120)


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