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Popular >

simplify ln(x^6e^{-6x})

Solution

simplify

ln (x^{6} e^{- 6 x})

Solution

6 ln (x) - 6 x

Solution steps

ln (x^{6} e^{- 6 x})

Apply log rule:

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

ln (x^{6} e^{- 6 x}) = ln (x^{6}) + ln (e^{- 6 x})

= ln (x^{6}) + ln (e^{- 6 x})

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= 6 ln (x) + ln (e^{- 6 x})

Apply log rule:

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

ln (e^{- 6 x}) = - 6 x ln (e)

= 6 ln (x) - 6 x ln (e)

6 x ln (e) = 6 x

= 6 ln (x) - 6 x

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Frequently Asked Questions (FAQ)

What is ln(x^6e^{-6x}) ?
The solution to ln(x^6e^{-6x}) is 6ln(x)-6x