en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

simplify

ln (x \cdot 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(x/(y^3))+ln(y^2)simplify

ln (\frac{x}{y ^{3}}) + ln (y^{2})

simplify 2ln|x-1|-ln|x+2|+C simplify

2 ln ∣ x - 1 ∣ - ln ∣ x + 2 ∣ + C

simplify-log_{10}(2.1*10^{-53})simplify

- lo g_{10} (2.1 \cdot 1 0^{- 53})

simplify ln(1.6296*pi)simplify

ln (1.6296 \cdot π)

simplify log_{e}(6x^2-2)-log_{e}(x^2)simplify

lo g_{e} (6 x^{2} - 2) - lo g_{e} (x^{2})

Frequently Asked Questions (FAQ)

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