simplify ln(x*e^x)

Solution

simplify

ln (x \cdot 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

2 lo g_{10} (x) - 4 lo g_{10} (y)

- lo g_{10} (6.3 \cdot 1 0^{- 3})

lo g_{2} (12 x^{5} y^{- 2})

lo g_{10} (B^{- 5})

x^{3} y^{3} z^{3} + ln (y^{5} z^{4})