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I have a question about Arduino, if I supply 4.5 V to Arduino and I declare the pin 13 as an output this voltage will be equal ?

If supply = 4.5V, OUTPUT = 4.5V
If supply = 3V,    OUTPUT = 3V
If supply = 3.5V, OUTPUT = 3.5V

I know it can be checked by a multimeter but I do not have one.
Thanks.
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Output voltage could be as low as 0.7v less than the supply up to the supply voltage.

This can be found on in the "Electrical Characteristics" of the ATmega328 data sheet.
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But with reasonably low loads, it should be about equal.
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