simplify ln(a*e^b)

Solution

simplify

ln (a \cdot e^{b})

ln (a) + b

Solution steps

ln (a e^{b})

Apply log rule:

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

ln (a e^{b}) = ln (a) + ln (e^{b})

= ln (a) + ln (e^{b})

Apply log rule:

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

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

= ln (a) + b ln (e)

b ln (e) = b

= ln (a) + b

2 ln (x + 2) - ln (x + 2) - ln (2) 3

ln (2^{x} (2 - x)^{5})

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

ln ∣ y ∣ - ln ∣ y - 1 ∣

- 0.2 \cdot lo g_{2} (0.2) - 0.8 \cdot lo g_{2} (0.8)