simplify ln(2e^y)

Solution

simplify

ln (2 e^{y})

ln (2) + y

Solution steps

ln (2 e^{y})

Apply log rule:

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

ln (2 e^{y}) = ln (2) + ln (e^{y})

= ln (2) + ln (e^{y})

Apply log rule:

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

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

= ln (2) + y ln (e)

y ln (e) = y

= ln (2) + y

ln (\frac{x}{y ^{3}})

ln (\frac{4 - x}{2 + 2 x})

ln (\frac{3 x}{x + 2})

3 ln (x) + \frac{1}{3} ln (x + 2)

ln (x^{3} yz)