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Popular >

simplify ln(9e^{-x})

Solution

simplify

ln (9 e^{- x})

Solution

2 ln (3) - x

Solution steps

ln (9 e^{- x})

Apply log rule:

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

ln (9 e^{- x}) = ln (9) + ln (e^{- x})

= ln (9) + ln (e^{- x})

Apply log rule:

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

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

= ln (9) - x ln (e)

x ln (e) = x

= ln (9) - x

ln (9) = 2 ln (3)

= 2 ln (3) - x

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Frequently Asked Questions (FAQ)

What is ln(9e^{-x}) ?
The solution to ln(9e^{-x}) is 2ln(3)-x