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Popular >

simplify ln(xe^{-x})

Solution

simplify

ln (x e^{- x})

Solution

ln (x) - x

Solution steps

ln (x e^{- x})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (x) - x ln (e)

x ln (e) = x

= ln (x) - x

Popular Examples

simplify (ln^2(x)+ln(x)-2)(log_{5}(x)-2)simplify

(ln^{2} (x) + ln (x) - 2) (lo g_{5} (x) - 2)

simplify 7log_{5}(x)+12log_{5}(y)simplify

7 lo g_{5} (x) + 12 lo g_{5} (y)

domain of f(x)=3log_{10}(x+5)-log_{10}(x-2)domain

f (x) = 3 lo g_{10} (x + 5) - lo g_{10} (x - 2)

simplify 1.1*ln(670/970)-(8.314)/(28.97)*ln(1/4)simplify

1.1 \cdot ln (\frac{670}{970}) - \frac{8.314}{28.97} \cdot ln (\frac{1}{4})

domain of f(x)=ln(2x^2-2x-24)-ln(-2x-6)domain

f (x) = ln (2 x^{2} - 2 x - 24) - ln (- 2 x - 6)

Frequently Asked Questions (FAQ)

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