simplify ln(2e^θ)

Solution

simplify

ln (2 e^{θ})

ln (2) + θ

Solution steps

ln (2 e^{θ})

Apply log rule:

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

ln (2 e^{θ}) = ln (2) + ln (e^{θ})

= ln (2) + ln (e^{θ})

Apply log rule:

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

ln (e^{θ}) = θ ln (e)

= ln (2) + θ ln (e)

θ ln (e) = θ

= ln (2) + θ

2 ln (x) - ln (1 - x)

ln (4 e^{2 t})

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

ln (\frac{1}{1 - 0.11})

ln (ab) - ln (a)