What is laplacetransform e^{5(t-2)} ?

The answer to laplacetransform e^{5(t-2)} is 1/(e^{10)(s-5)}

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laplacetransform e^{5(t-2)}

laplace transform

e^{5 (t - 2)}

\frac{1}{e ^{10} ( s - 5 )}

Solution steps

L {e^{5 (t - 2)}}

Expand

e^{5 (t - 2)} : e^{5 t - 10}

= L {e^{5 t - 10}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= e^{- 10} L {e^{5 t}}

L {e^{5 t}} : \frac{1}{s - 5}

= e^{- 10} \frac{1}{s - 5}

Refine

e^{- 10} \frac{1}{s - 5} : \frac{1}{e ^{10} ( s - 5 )}

= \frac{1}{e ^{10} ( s - 5 )}

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What is laplacetransform e^{5(t-2)} ?
The answer to laplacetransform e^{5(t-2)} is 1/(e^{10)(s-5)}