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Popular >

simplify ln(y^xe^{-y})

Solution

simplify

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

Solution

x ln (y) - y

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

y ln (e) = y

= x ln (y) - y

Popular Examples

simplify log_{2}(0.05)+log_{2}(0.9)simplify

lo g_{2} (0.05) + lo g_{2} (0.9)

join 1+1/(50000ln(5))join

1 + \frac{1}{50000 ln ( 5 )}

simplify ln((10^2)/(8^2))simplify

ln (\frac{1 0 ^{2}}{8 ^{2}})

simplify 2.06*ln(2/1)simplify

2.06 \cdot ln (\frac{2}{1})

simplify ln(0.6*pi)simplify

ln (0.6 \cdot π)

Frequently Asked Questions (FAQ)

What is ln(y^xe^{-y}) ?
The solution to ln(y^xe^{-y}) is xln(y)-y