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Popular >

simplify ln(ke^{-bk}b^2)

Solution

simplify

ln (k e^{- bk} b^{2})

Solution

ln (k) - bk + 2 ln (b)

Solution steps

ln (k e^{- bk} b^{2})

Apply log rule:

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

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

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

Apply log rule:

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

ln (e^{- bk}) = - bk ln (e)

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

Apply log rule:

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

ln (b^{2}) = 2 ln (b)

= ln (k) - bk ln (e) + 2 ln (b)

bk ln (e) = bk

= ln (k) - bk + 2 ln (b)

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Frequently Asked Questions (FAQ)

What is ln(ke^{-bk}b^2) ?
The solution to ln(ke^{-bk}b^2) is ln(k)-bk+2ln(b)