Simplify e^(x+lnx) ?

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Answer 1 · 2017-07-17T18:09:58

Note that, #e^x=y iff lny=x.#

#rArr e^(lny)=y.#

# :. e^(x+lnx)=e^x*e^(lnx)=e^x*x=xe^x.#

Answer 2 · 2017-07-17T18:10:09

See below.

#e^(x+log_e x)= e^x * e^(log_e x) = e^x*x = W(x)#

then

#e^(x+log_e x)=W(x)# where #W( cdot)# is the Lambert function.