Which is the smallest of these surd, log and trig expressions?

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Which is the smallest of the following numbers?

1. \(\left(\sqrt{3}\right)^3\),

2. \(\log_3 \left(9^2\right)\),

3. \(\left( 3\sin{\dfrac{\pi}{3}}\right) ^2\),

4. \(\log_2 \left(\log_2 \left(8^5\right)\right)\).

Can we evaluate any of the expressions exactly?

If so, how do the other expressions compare with the exact value(s)?