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Popular >

simplify ln(xe^{-2x})

Solution

simplify

ln (x e^{- 2 x})

Solution

ln (x) - 2 x

Solution steps

ln (x e^{- 2 x})

Apply log rule:

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

ln (x e^{- 2 x}) = ln (x) + ln (e^{- 2 x})

= ln (x) + ln (e^{- 2 x})

Apply log rule:

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

ln (e^{- 2 x}) = - 2 x ln (e)

= ln (x) - 2 x ln (e)

2 x ln (e) = 2 x

= ln (x) - 2 x

Popular Examples

domain of f(x)=ln(x^6)-4ln(\sqrt[4]{x^5})domain

domain of f(x)=log_{10}(9x^4)+log_{10}(5x^5)domain

f (x) = lo g_{10} (9 x^{4}) + lo g_{10} (5 x^{5})

domain of f(x)=log_{3}(sqrt(x))-log_{3}(x^9)domain

f (x) = lo g_{3} (x) - lo g_{3} (x^{9})

simplify 192ln(192/762)-192+763 simplify

192 ln (\frac{192}{762}) - 192 + 763

simplify log_{10}((y^8)/z)simplify

lo g_{10} (\frac{y ^{8}}{z})

Frequently Asked Questions (FAQ)

What is ln(xe^{-2x}) ?
The solution to ln(xe^{-2x}) is ln(x)-2x