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

The solution to (e^{-t}ln(t))(e^{-t}) is e^{-2t}ln(t)

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

simplify

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

e^{- 2 t} ln (t)

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- t} e^{- t} = e^{- t - t}

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

Add similar elements:

- t - t = - 2 t

= ln (t) e^{- 2 t}

\frac{9.787604}{2 \cdot ( - 2.36621 )}

- 10 \cdot e^{- 2}

1.15 \cdot 1 0^{- 3}

20 2^{2}

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