What is log_{e}(2*a*x^{-ax^2}) ?

The solution to log_{e}(2*a*x^{-ax^2}) is ln(2)+ln(a)-ax^2ln(x)

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simplify log_{e}(2ax^{-ax^2})

simplify

lo g_{e} (2 \cdot a \cdot x^{- a x^{2}})

ln (2) + ln (a) - a x^{2} ln (x)

Solution steps

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

Apply log rule:

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

lo g_{e} (2 a x^{- a x^{2}}) = lo g_{e} (2) + lo g_{e} (a) + lo g_{e} (x^{- a x^{2}})

= lo g_{e} (2) + lo g_{e} (a) + lo g_{e} (x^{- a x^{2}})

Apply log rule:

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

lo g_{e} (x^{- a x^{2}}) = - a x^{2} lo g_{e} (x)

= lo g_{e} (2) + lo g_{e} (a) - a x^{2} lo g_{e} (x)

Apply log rule:

lo g_{e} (x) = ln (x)

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

Apply log rule:

lo g_{e} (x) = ln (x)

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

Simplify

lo g_{e} (x) : ln (x)

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

ln (\frac{1}{e ^{6}}) + ln (6) e^{3}

ln (x - 2) - ln (x + 3)

ln (x^{2} (x + 8) 8 (x^{2} + 7) 8)

- \frac{1}{2} ln (\frac{y}{2})

ln (x sin^{4} (x))

What is log_{e}(2*a*x^{-ax^2}) ?
The solution to log_{e}(2*a*x^{-ax^2}) is ln(2)+ln(a)-ax^2ln(x)