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Popular >

simplify ln(12te^{-6t})

Solution

simplify

ln (12 t e^{- 6 t})

Solution

ln (12) + ln (t) - 6 t

Solution steps

ln (12 t e^{- 6 t})

Apply log rule:

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

ln (12 t e^{- 6 t}) = ln (12) + ln (t) + ln (e^{- 6 t})

= ln (12) + ln (t) + ln (e^{- 6 t})

Apply log rule:

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

ln (e^{- 6 t}) = - 6 t ln (e)

= ln (12) + ln (t) - 6 t ln (e)

6 t ln (e) = 6 t

= ln (12) + ln (t) - 6 t

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Frequently Asked Questions (FAQ)

What is ln(12te^{-6t}) ?
The solution to ln(12te^{-6t}) is ln(12)+ln(t)-6t