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Popular >

simplify ln(x^5*e^{-3x})

Solution

simplify

ln (x^{5} \cdot e^{- 3 x})

Solution

5 ln (x) - 3 x

Solution steps

ln (x^{5} e^{- 3 x})

Apply log rule:

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

ln (x^{5} e^{- 3 x}) = ln (x^{5}) + ln (e^{- 3 x})

= ln (x^{5}) + ln (e^{- 3 x})

Apply log rule:

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

ln (x^{5}) = 5 ln (x)

= 5 ln (x) + ln (e^{- 3 x})

Apply log rule:

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

ln (e^{- 3 x}) = - 3 x ln (e)

= 5 ln (x) - 3 x ln (e)

3 x ln (e) = 3 x

= 5 ln (x) - 3 x

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Frequently Asked Questions (FAQ)

What is ln(x^5*e^{-3x}) ?
The solution to ln(x^5*e^{-3x}) is 5ln(x)-3x