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Popular >

simplify ln(0.5te^{-0.5t})

Solution

simplify

ln (0.5 t e^{- 0.5 t})

Solution

ln (0.5) + ln (t) - 0.5 t

Solution steps

ln (0.5 t e^{- 0.5 t})

Apply log rule:

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

ln (0.5 t e^{- 0.5 t}) = ln (0.5) + ln (t) + ln (e^{- 0.5 t})

= ln (0.5) + ln (t) + ln (e^{- 0.5 t})

Apply log rule:

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

ln (e^{- 0.5 t}) = - 0.5 t ln (e)

= ln (0.5) + ln (t) - 0.5 t ln (e)

0.5 t ln (e) = 0.5 t

= ln (0.5) + ln (t) - 0.5 t

Popular Examples

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Frequently Asked Questions (FAQ)

What is ln(0.5te^{-0.5t}) ?
The solution to ln(0.5te^{-0.5t}) is ln(0.5)+ln(t)-0.5t