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Question Number 164279 by amin96 last updated on 15/Jan/22
xn=nxx=?
Answered by Saiki last updated on 15/Jan/22
lnxn=lnnxnlnx=xlnnlnxx=lnnnx−1lnx=lnnnelnx−1lnx=lnnne−lnxlnx=lnnn−lnxe−lnx=−lnnnW(−lnxe−lnx)=W(−lnnn)−lnx=W(−lnnn)x=e−W(−lnnn)solutionbyCASIO......
Answered by MathsFan last updated on 15/Jan/22
x∙n−xn=1xlnn∙e−xnlnn=lnn−xlnnn∙e−xnlnn=−lnnn−xlnnn=W(−lnnn)x=−nW(−lnnn)lnn
Answered by mr W last updated on 15/Jan/22
ifn=eveninteger:e.g.x2=2xx=±nxnx=±exnlnn(−xnlnn)e−xnlnn=±lnnn(−xnlnn)=W(±lnnn)⇒x=−nlnnW(±lnnn)similarly,ifn≠eveninteger,e.g.x3=3x:⇒x=−nlnnW(−lnnn)
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