simplify ln(3e^t)

Solution

simplify

ln (3 e^{t})

ln (3) + t

Solution steps

ln (3 e^{t})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (3) + t ln (e)

t ln (e) = t

= ln (3) + t

2 ln (7) - 2 ln (2)

ln (\frac{1}{0.75})

ln (5) + 3 ln (x) + 6 ln (x^{2} + 9)

ln (4 e^{\frac{2 π x}{3}})

ln (\frac{1073.15}{273.15})