simplify ln(2x*e^x)

Solution

simplify

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

ln (2) + ln (x) + x

Solution steps

ln (2 x e^{x})

Apply log rule:

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

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

= ln (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)

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

x ln (e) = x

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

ln (x^{- 5}) - 5 ln (y)

ln (x y z)

ln (\frac{6}{8})

ln (\frac{38628147}{16456158})

ln (\frac{0.13}{0.1})