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Popular >

simplify ln((e^{-5k})/k)

Solution

simplify

ln (\frac{e ^{- 5 k}}{k})

Solution

- 5 k - ln (k)

Solution steps

ln (\frac{e ^{- 5 k}}{k})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{e ^{- 5 k}}{k}) = ln (e^{- 5 k}) - ln (k)

= ln (e^{- 5 k}) - ln (k)

Apply log rule:

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

ln (e^{- 5 k}) = - 5 k ln (e)

= - 5 k ln (e) - ln (k)

5 k ln (e) = 5 k

= - 5 k - ln (k)

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Frequently Asked Questions (FAQ)

What is ln((e^{-5k})/k) ?
The solution to ln((e^{-5k})/k) is -5k-ln(k)