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Popular >

simplify ln(e^{-y}*y^x)

Solution

simplify

ln (e^{- y} \cdot y^{x})

Solution

- y + x ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (y^{x}) = x ln (y)

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

y ln (e) = y

= - y + x ln (y)

Popular Examples

simplify-8ln(1/2)+4 simplify

- 8 ln (\frac{1}{2}) + 4

join 1/7 ln(2)join

\frac{1}{7} ln (2)

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2 ln (5) + ln (10) - \frac{1}{2} ln (4)

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ln (x^{7}) - ln (x)

simplify log_{10}((3z)/(10))simplify

lo g_{10} (\frac{3 z}{10})

Frequently Asked Questions (FAQ)

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