What is ln(Ae^{3/2 t^2}) ?

The solution to ln(Ae^{3/2 t^2}) is ln(A)+(3t^2)/2

Popular >

simplify ln(Ae^{3/2 t^2})

simplify

ln (A e^{\frac{3}{2} t^{2}})

ln (A) + \frac{3 t ^{2}}{2}

Solution steps

ln (A e^{\frac{3}{2} t^{2}})

Apply log rule:

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

ln (A e^{\frac{3}{2} t^{2}}) = ln (A) + ln (e^{\frac{3}{2} t^{2}})

= ln (A) + ln (e^{\frac{3}{2} t^{2}})

Apply log rule:

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

ln (e^{\frac{3}{2} t^{2}}) = \frac{3}{2} t^{2} ln (e)

= ln (A) + \frac{3}{2} t^{2} ln (e)

\frac{3}{2} t^{2} ln (e) = \frac{3 t ^{2}}{2}

= ln (A) + \frac{3 t ^{2}}{2}

ln ∣ 4 ∣ + 2 ln (4^{2} + 4) - ln ∣ 1 ∣ + 2 ln (1^{2} + 4)

ln (w) + 6 ln (u) - 2 ln (v)

\frac{9}{2} ln (\frac{3}{2}) + \frac{3}{8} - ln (2) - ln (2)

182000 (ln (0.79) - ln (1.3))