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Popular >

simplify ln(1000e^{-x})

Solution

simplify

ln (1000 e^{- x})

Solution

3 ln (10) - x

Solution steps

ln (1000 e^{- x})

Apply log rule:

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

ln (1000 e^{- x}) = ln (1000) + ln (e^{- x})

= ln (1000) + ln (e^{- x})

Apply log rule:

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

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

= ln (1000) - x ln (e)

x ln (e) = x

= ln (1000) - x

ln (1000) = 3 ln (10)

= 3 ln (10) - x

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Frequently Asked Questions (FAQ)

What is ln(1000e^{-x}) ?
The solution to ln(1000e^{-x}) is 3ln(10)-x