simplify ln(2xe^x)

Solution

simplify

ln (2 x 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

lo g_{10} (4) + lo g_{10} (7)

lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (x y)

ln (\frac{1}{2 ^{3}})

ln (\frac{37}{125})