simplify ln(e^xx)

Solution

simplify

ln (e^{x} 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)

- ln (3) + 2 ln (2)

lo g_{a} (\frac{x + y}{z})

ln (4 x)

lo g_{10} (\frac{x ^{2} + 9}{x + 3})

lo g_{b} (x^{4} y)