simplify ln(ye^y)

Solution

simplify

ln (y e^{y})

ln (y) + y

Solution steps

ln (y e^{y})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (y) + y ln (e)

y ln (e) = y

= ln (y) + y

\frac{3 ln ( 2 )}{ln ( 3 )} - 1

f (x) = ln (\frac{x + 2}{x + 1})

3 ln (a) - 2 ln (b) - 4 ln (c)

f (m) = 2 ln (m) + ln (6 m)

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