simplify ln(-2e^x)

Solution

simplify

ln (- 2 e^{x})

ln (2) + x

Solution steps

ln (- 2 e^{x})

Apply log rule:

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

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

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

x ln (e) = x

= ln (2) + x

ln (e^{4 x} arctan (x^{2}))

ln (4) + 3 ln (3)

lo g_{e} (5 e^{2 x})

2 ln (x + 2) - ln (x)

3 ln (x) - ln (x + 1)