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Popular >

simplify ln(e^{-3x}x)

Solution

simplify

ln (e^{- 3 x} x)

Solution

- 3 x + ln (x)

Solution steps

ln (e^{- 3 x} x)

Apply log rule:

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

ln (e^{- 3 x} x) = ln (e^{- 3 x}) + ln (x)

= ln (e^{- 3 x}) + ln (x)

Apply log rule:

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

ln (e^{- 3 x}) = - 3 x ln (e)

= - 3 x ln (e) + ln (x)

3 x ln (e) = 3 x

= - 3 x + ln (x)

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Frequently Asked Questions (FAQ)

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