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Popular >

simplify ln((e^{-3y})/3)

Solution

simplify

ln (\frac{e ^{- 3 y}}{3})

Solution

- 3 y - ln (3)

Solution steps

ln (\frac{e ^{- 3 y}}{3})

Apply log rule:

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

ln (\frac{e ^{- 3 y}}{3}) = ln (e^{- 3 y}) - ln (3)

= ln (e^{- 3 y}) - ln (3)

Apply log rule:

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

ln (e^{- 3 y}) = - 3 y ln (e)

= - 3 y ln (e) - ln (3)

3 y ln (e) = 3 y

= - 3 y - ln (3)

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Frequently Asked Questions (FAQ)

What is ln((e^{-3y})/3) ?
The solution to ln((e^{-3y})/3) is -3y-ln(3)