simplify ln(e^x*x)

Solution

simplify

ln (e^{x} \cdot x)

x + ln (x)

Solution steps

ln (e^{x} x)

Apply log rule:

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

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

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

Apply log rule:

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

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

= x ln (e) + ln (x)

x ln (e) = x

= x + ln (x)

lo g_{10} (\frac{g j ^{5} k}{100})

ln (\frac{5}{2})

3 ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ + \frac{8}{x + 1} + C

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

ln (\frac{47}{50}) + \frac{1}{47}