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Question Number 9875 by j.masanja06@gmail.com last updated on 11/Jan/17
solve the value of x. 5logx=(x/4)
solvethevalueofx.5logx=x4
Answered by mrW1 last updated on 12/Jan/17
5log x=(x/4) log x=(x/(20)) ((ln x)/(ln 10))=(x/(20)) ln x=((ln 10)/(20))x with a=−((ln 10)/(20))≈−0.115129 ln x=−ax x=e^(−ax) =(1/e^(ax) ) xe^(ax) =1 (ax)e^(ax) =a ⇒ax=W(a) with W=Lambert W function x=((W(a))/a)=((W(−((ln 10)/(20))))/(−((ln 10)/(20))))≈((W(−0.115129))/(−0.115129)) ≈((−0.13128)/(−0.115129))≈1.140286 or ≈((−3.3794)/(−0.115128))≈29.35316
5logx=x4logx=x20lnxln10=x20lnx=ln1020xwitha=−ln1020≈−0.115129lnx=−axx=e−ax=1eaxxeax=1(ax)eax=a⇒ax=W(a)withW=LambertWfunctionx=W(a)a=W(−ln1020)−ln1020≈W(−0.115129)−0.115129≈−0.13128−0.115129≈1.140286or≈−3.3794−0.115128≈29.35316

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