simplify ln(x^2e^x)

Solution

simplify

ln (x^{2} e^{x})

2 ln (x) + x

Solution steps

ln (x^{2} e^{x})

Apply log rule:

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

ln (x^{2} e^{x}) = ln (x^{2}) + ln (e^{x})

= ln (x^{2}) + ln (e^{x})

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= 2 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)

= 2 ln (x) + x ln (e)

x ln (e) = x

= 2 ln (x) + x

lo g_{10} (\frac{40}{9}) + 4 lo g_{10} (5) + 2 lo g_{10} (6)

2 - lo g_{5} (\frac{1}{16}) - \frac{1}{3} lo g_{5} (8)

5 ln (x) + 4 ln (y) - 2 ln (z)

ln (\frac{x + 2}{x - 3})

4 ln (2) - \frac{1}{2} ln (25)