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Popular >

simplify ln(e^{-y}sin(y))

Solution

simplify

ln (e^{- y} sin (y))

Solution

- y + ln (sin (y))

Solution steps

ln (e^{- y} sin (y))

Apply log rule:

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

ln (e^{- y} sin (y)) = ln (e^{- y}) + ln (sin (y))

= ln (e^{- y}) + ln (sin (y))

Apply log rule:

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

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

= - y ln (e) + ln (sin (y))

y ln (e) = y

= - y + ln (sin (y))

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Frequently Asked Questions (FAQ)

What is ln(e^{-y}sin(y)) ?
The solution to ln(e^{-y}sin(y)) is -y+ln(sin(y))