The Laplace transformation of $\delta(2t-3)$?

Question

I know the Laplace transformation of the unit impulse function $\delta(t)$,but what about the Laplace transformation of $\delta(2t-3)$. Are there any special property of this function I don't know?

Answer 1

Use the following:

$$\mathcal{L}\{\delta(t)\}=1$$

$$\mathcal{L}\{f(t-a)\}=e^{-as}F(s)$$

$$\mathcal{L}\{f(at)\}=\frac{1}{|a|}F(\frac{s}{a})$$

to get

$$\mathcal{L}\{\delta(2t-3)\}=\frac{1}{2}e^{-3s/2}$$