What is ln(600t^3e^{-78.5t}) ?

The solution to ln(600t^3e^{-78.5t}) is ln(600)+3ln(t)-78.5t

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simplify ln(600t^3e^{-78.5t})

simplify

ln (600 t^{3} e^{- 78.5 t})

ln (600) + 3 ln (t) - 78.5 t

Solution steps

ln (600 t^{3} e^{- 78.5 t})

Apply log rule:

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

ln (600 t^{3} e^{- 78.5 t}) = ln (600) + ln (t^{3}) + ln (e^{- 78.5 t})

= ln (600) + ln (t^{3}) + ln (e^{- 78.5 t})

Apply log rule:

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

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

= ln (600) + 3 ln (t) + ln (e^{- 78.5 t})

Apply log rule:

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

ln (e^{- 78.5 t}) = - 78.5 t ln (e)

= ln (600) + 3 ln (t) - 78.5 t ln (e)

78.5 t ln (e) = 78.5 t

= ln (600) + 3 ln (t) - 78.5 t

- ln (\frac{0.79}{1.21 \cdot 1 0 ^{4}})

ln ((- 1.1) (- 1.8))

lo g_{e} ((1 + θ) x^{θ})

3 ln (x^{4} e^{x^{3}})

What is ln(600t^3e^{-78.5t}) ?
The solution to ln(600t^3e^{-78.5t}) is ln(600)+3ln(t)-78.5t