If y=1−x+x^2/(2!)−x^3/(3!)+… and z=−y−y^2/2−y^3/3−… then ln(1/(1−e^x))

Meossi91 2022-08-11 Answered
If y = 1 x + x 2 2 ! x 3 3 ! + and z = y y 2 2 y 3 3 then ln ( 1 1 e x )
I can see that y = e x and z = ln ( 1 y ) . And, so z = ln ( 1 e x ). But how to go further?
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Answers (1)

Ben Logan
Answered 2022-08-12 Author has 13 answers
Once you know that z = log ( 1 e x ), you immediately have that
log ( 1 1 e z ) = log ( 1 1 e log ( 1 e x ) ) = log ( 1 1 ( 1 e x ) ) = log ( 1 e x ) = log e x = x
And you've done.
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