simplify ln(x^ee^x)

Solution

simplify

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

e ln (x) + x

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= e 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)

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

x ln (e) = x

= e ln (x) + x

ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ + ln ∣ x - 2 ∣ + C

lo g_{3} (\frac{81}{y})

2 ln (3) - 2 ln (2)

lo g_{2} (\frac{8 X ^{3}}{2 Y})

lo g_{10} (a) + 3 lo g_{10} (2 b)