simplify ln(ae^b)

Solution

simplify

ln (a 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

lo g_{2} (45) - lo g_{2} (5)

lo g_{2} (\frac{x ^{3} y}{5 z ^{6}})

- 4 lo g_{b} (d) + lo g_{b} (e) - 2 lo g_{b} (f)

lo g_{10} (\frac{3 x}{y})

ln ∣ b ∣ - ln ∣ a ∣