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Popular >

simplify ln(-5ae^{-5a})

Solution

simplify

ln (- 5 a e^{- 5 a})

Solution

ln (5) + ln (a) - 5 a

Solution steps

ln (- 5 a e^{- 5 a})

Apply log rule:

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

ln (- 5 a e^{- 5 a}) = ln (5) + ln (a) + ln (e^{- 5 a})

= ln (5) + ln (a) + ln (e^{- 5 a})

Apply log rule:

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

ln (e^{- 5 a}) = - 5 a ln (e)

= ln (5) + ln (a) - 5 a ln (e)

5 a ln (e) = 5 a

= ln (5) + ln (a) - 5 a

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Frequently Asked Questions (FAQ)

What is ln(-5ae^{-5a}) ?
The solution to ln(-5ae^{-5a}) is ln(5)+ln(a)-5a