What is ln((x-1)^x)+ln(e^{-x}) ?

The solution to ln((x-1)^x)+ln(e^{-x}) is ln((x-1)^xe^{-x})

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simplify ln((x-1)^x)+ln(e^{-x})

simplify

ln ((x - 1)^{x}) + ln (e^{- x})

ln ((x - 1)^{x} e^{- x})

Solution steps

ln ((x - 1)^{x}) + ln (e^{- x})

Apply log rule:

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

ln ((x - 1)^{x}) + ln (e^{- x}) = ln (e^{- x} (x - 1)^{x})

= ln ((x - 1)^{x} e^{- x})

- lo g_{10} (3.6 \cdot 1 0^{- 7})

ln (x^{2} 1 0^{2 x})

2 lo g_{a} (x) - 6 lo g_{a} (y)

5 lo g_{a} (x) - 2 lo g_{a} (y)

ln (3 ln (2))

What is ln((x-1)^x)+ln(e^{-x}) ?
The solution to ln((x-1)^x)+ln(e^{-x}) is ln((x-1)^xe^{-x})