simplify ln(3ye^y)

Solution

simplify

ln (3 y e^{y})

ln (3) + ln (y) + y

Solution steps

ln (3 y e^{y})

Apply log rule:

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

ln (3 y e^{y}) = ln (3) + ln (y) + ln (e^{y})

= ln (3) + 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 (3) + ln (y) + y ln (e)

y ln (e) = y

= ln (3) + ln (y) + y

ln (2 e^{- 7 x})

ln (100 x^{2})

lo g_{10} ((a + b) (a - b)^{2})

2 ln (x^{3} y \frac{1}{2})

lo g_{2} (49.92) - lo g_{2} (6.24)