simplify ln(2e^β)

Solution

simplify

ln (2 e^{β})

ln (2) + β

Solution steps

ln (2 e^{β})

Apply log rule:

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

ln (2 e^{β}) = ln (2) + ln (e^{β})

= ln (2) + ln (e^{β})

Apply log rule:

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

ln (e^{β}) = β ln (e)

= ln (2) + β ln (e)

β ln (e) = β

= ln (2) + β

ln \frac{y}{x} - \frac{y}{x} + ln ∣ x ∣

ln (\frac{45.5}{6.26})

ln (\frac{2000}{70})

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

lo g_{10} (\frac{[ 0.73 ]}{[ 0.39 ]}) + 9.252