What is ln(3/2 ae^{-3/2 ax}) ?

The solution to ln(3/2 ae^{-3/2 ax}) is ln(3)-ln(2)+ln(a)-(3ax)/2

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simplify ln(3/2 ae^{-3/2 ax})

simplify

ln (\frac{3}{2} a e^{- \frac{3}{2} a x})

ln (3) - ln (2) + ln (a) - \frac{3 a x}{2}

Solution steps

ln (\frac{3}{2} a e^{- \frac{3}{2} a x})

Apply log rule:

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

ln (\frac{3}{2} a e^{- \frac{3}{2} a x}) = ln (\frac{3}{2}) + ln (a) + ln (e^{- \frac{3}{2} a x})

= ln (\frac{3}{2}) + ln (a) + ln (e^{- \frac{3}{2} a x})

Apply log rule:

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

ln (e^{- \frac{3}{2} a x}) = - \frac{3}{2} a x ln (e)

= ln (\frac{3}{2}) + ln (a) - \frac{3}{2} a x ln (e)

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{3}{2}) = ln (3) - ln (2)

= ln (3) - ln (2) + ln (a) - \frac{3}{2} ln (e) a x

\frac{3}{2} a x ln (e) = \frac{3 a x}{2}

= ln (3) - ln (2) + ln (a) - \frac{3 a x}{2}

ln (2) - 2 ln (6)

2 ln (x) + \frac{1}{2} ln (x - 1) - 3 ln (x + 7)

\frac{1}{24} ln cos (3 x^{2})

\frac{1}{3} lo g_{10} (5)

0.77 - \frac{8.134 \cdot 298}{1 \cdot 96500} \cdot ln (\frac{1}{4})

What is ln(3/2 ae^{-3/2 ax}) ?
The solution to ln(3/2 ae^{-3/2 ax}) is ln(3)-ln(2)+ln(a)-(3ax)/2