a) 1
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Simplify in the following steps, using log rules:
- log₅45 - 2log₅3 = Given
- log₅(3*3*5) - 2log₅3 = Rule log(ab) = log(a) + log(b)
- 2log₅3 + log₅5 - 2log₅3 = Cancel equal terms with opposite signs
- log₅5 = Rule logₐ(a) = 1
- 1
So, the answer is 1.