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Popular >

simplify e^{-(x-1+ln|x-1|)}

Solution

simplify

e^{- (x - 1 + l n ∣ x - 1 ∣)}

Solution

\frac{1}{e ^{x - 1} ∣ x - 1 ∣}

Solution steps

e^{- (x - 1 + l n ∣ x - 1 ∣)}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{(x - 1 + l n ∣ x - 1 ∣)}}

Remove parentheses:

(a) = a

= \frac{1}{e ^{x - 1 + l n ∣ x - 1 ∣}}

e^{x - 1 + l n ∣ x - 1 ∣} = e^{x - 1} ∣ x - 1 ∣

= \frac{1}{e ^{x - 1} ∣ x - 1 ∣}

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Frequently Asked Questions (FAQ)

What is e^{-(x-1+ln|x-1|)} ?
The solution to e^{-(x-1+ln|x-1|)} is 1/(e^{x-1)|x-1|}