simplify ln(x^3e^x)

Solution

simplify

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

3 ln (x) + x

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 3 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)

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

x ln (e) = x

= 3 ln (x) + x

lo g_{e} (12) - lo g_{e} (6)

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

7 lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

ln (\frac{x ^{2} - 4 + x}{2})

ln (2 x) \cdot 2