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Popular >

simplify ln(7*e^{-x+5})

Solution

simplify

ln (7 \cdot e^{- x + 5})

Solution

ln (7) - x + 5

Solution steps

ln (7 e^{- x + 5})

Apply log rule:

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

ln (7 e^{- x + 5}) = ln (7) + ln (e^{- x + 5})

= ln (7) + ln (e^{- x + 5})

Apply log rule:

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

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

= ln (7) + (- x + 5) ln (e)

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

= ln (7) + (- x + 5)

Remove parentheses:

(- a) = - a

= ln (7) - x + 5

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Frequently Asked Questions (FAQ)

What is ln(7*e^{-x+5}) ?
The solution to ln(7*e^{-x+5}) is ln(7)-x+5