simplify ln(-xe^x)

Solution

simplify

ln (- x e^{x})

ln (x) + x

Solution steps

ln (- x e^{x})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (x) + x ln (e)

x ln (e) = x

= ln (x) + x

6 lo g_{10} (y) + 3 lo g_{10} (x)

lo g_{b} (\frac{1}{x})

\frac{1}{3} ln (x) + \frac{10}{12} ln (x + 3) - \frac{1}{6} ln (x + 3)

ln (\frac{350}{400 - x})

- ln (2) + ln (11) - ln (10) - ln (55)