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Popular >

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

Solution

simplify

(e^{- l n ∣ x ∣})^{1}

Solution

\frac{1}{∣ x ∣}

Solution steps

(e^{- l n ∣ x ∣})^{1}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= e^{(- l n ∣ x ∣) \cdot 1}

Simplify

(- ln ∣ x ∣) \cdot 1 : - ln ∣ x ∣

= e^{- l n ∣ x ∣}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

= (e^{l n ∣ x ∣})^{- 1}

Apply log rule:

a^{l o g_{a} (b)} = b

e^{l n ∣ x ∣} = ∣ x ∣

= ∣ x ∣^{- 1}

Apply exponent rule:

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

= \frac{1}{∣ x ∣}

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Frequently Asked Questions (FAQ)

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