Log3 45 +log3 900-log3 500

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To simplify this expression, we can use the properties of logarithms:

log3 45 + log3 900 - log3 500
= log3 (45900) - log3 500 (using the property log(a) + log(b) = log(ab))
= log3 40500 - log3 500
= log3 (40500/500) (using the property log(a) - log(b) = log(a/b))
= log3 81
= 4

Therefore, log3 45 + log3 900 - log3 500 simplifies to 4.