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Popular >

simplify ln(0.8e^{-x}x)

Solution

simplify

ln (0.8 e^{- x} x)

Solution

ln (0.8) - x + ln (x)

Solution steps

ln (0.8 e^{- x} x)

Apply log rule:

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

ln (0.8 e^{- x} x) = ln (0.8) + ln (e^{- x}) + ln (x)

= ln (0.8) + ln (e^{- x}) + ln (x)

Apply log rule:

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

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

= ln (0.8) - x ln (e) + ln (x)

x ln (e) = x

= ln (0.8) - x + ln (x)

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Frequently Asked Questions (FAQ)

What is ln(0.8e^{-x}x) ?
The solution to ln(0.8e^{-x}x) is ln(0.8)-x+ln(x)