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Popular >

simplify ln(-3/5 e^{-5t})

Solution

simplify

ln (- \frac{3}{5} e^{- 5 t})

Solution

ln (3) - ln (5) - 5 t

Solution steps

ln (- \frac{3}{5} e^{- 5 t})

Apply log rule:

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

ln (- \frac{3}{5} e^{- 5 t}) = ln (\frac{3}{5}) + ln (e^{- 5 t})

= ln (\frac{3}{5}) + ln (e^{- 5 t})

Apply log rule:

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

ln (e^{- 5 t}) = - 5 t ln (e)

= ln (\frac{3}{5}) - 5 t ln (e)

Apply log rule:

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

ln (\frac{3}{5}) = ln (3) - ln (5)

= ln (3) - ln (5) - 5 ln (e) t

5 t ln (e) = 5 t

= ln (3) - ln (5) - 5 t

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Frequently Asked Questions (FAQ)

What is ln(-3/5 e^{-5t}) ?
The solution to ln(-3/5 e^{-5t}) is ln(3)-ln(5)-5t