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Popular >

simplify ln(2*e^{-10k})

Solution

simplify

ln (2 \cdot e^{- 10 k})

Solution

ln (2) - 10 k

Solution steps

ln (2 e^{- 10 k})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 e^{- 10 k}) = ln (2) + ln (e^{- 10 k})

= ln (2) + ln (e^{- 10 k})

Apply log rule:

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

ln (e^{- 10 k}) = - 10 k ln (e)

= ln (2) - 10 k ln (e)

10 k ln (e) = 10 k

= ln (2) - 10 k

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Frequently Asked Questions (FAQ)

What is ln(2*e^{-10k}) ?
The solution to ln(2*e^{-10k}) is ln(2)-10k