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Popular >

simplify ln(9*e^{-3t})

Solution

simplify

ln (9 \cdot e^{- 3 t})

Solution

2 ln (3) - 3 t

Solution steps

ln (9 e^{- 3 t})

Apply log rule:

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

ln (9 e^{- 3 t}) = ln (9) + ln (e^{- 3 t})

= ln (9) + ln (e^{- 3 t})

Apply log rule:

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

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

= ln (9) - 3 t ln (e)

3 t ln (e) = 3 t

= ln (9) - 3 t

ln (9) = 2 ln (3)

= 2 ln (3) - 3 t

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Frequently Asked Questions (FAQ)

What is ln(9*e^{-3t}) ?
The solution to ln(9*e^{-3t}) is 2ln(3)-3t