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Popular >

simplify ln(1/(e^x))

Solution

simplify

ln (\frac{1}{e ^{x}})

Solution

- x

Solution steps

ln (\frac{1}{e ^{x}})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (e^{x})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= - ln (e) x

Apply log rule:

lo g_{a} (a) = 1

= - x

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Frequently Asked Questions (FAQ)

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