What is ln((a^3)/2 x^2e^{-3a}) ?

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

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simplify ln((a^3)/2 x^2e^{-3a})

simplify

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

3 ln (a) - ln (2) + 2 ln (x) - 3 a

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

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

Apply log rule:

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

ln (e^{- 3 a}) = - 3 a ln (e)

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (a^{3}) = 3 ln (a)

= 3 ln (a) - ln (2) + 2 ln (x) - 3 a ln (e)

3 a ln (e) = 3 a

= 3 ln (a) - ln (2) + 2 ln (x) - 3 a

ln (- 0.333) - ln (- \frac{1.2502}{3})

ln ((1 + b t) e^{- b t})

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

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

3 lo g_{7} (x) + 2 lo g_{7} (z)

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