Arturo, 49 bytes

f:$->n->(n>1)?[map[2,3,4,5]=>[+1+f//n<=&]|min]->0

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Port of xnor's 50-byte Python answer.

Arturo, 71 bytes

$->n->min map[0 1 3 2 7 6 4 3 8 9 12 27 16 81 6 5]=>[&+5*ceil log//n&4]

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The formula in the OP.

Arturo, ⁴⁹ 45 bytes

f:$->n->(n>1)?[2..5|map=>[+1+f//n<=&]|min]->0

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Port of xnor's 50-byte Python answer.

Arturo, 71 bytes

$->n->min map[0 1 3 2 7 6 4 3 8 9 12 27 16 81 6 5]=>[&+5*ceil log//n&4]

Try it!

The formula in the OP.

Arturo, 71 bytes

$->n->min map[0 1 3 2 7 6 4 3 8 9 12 27 16 81 6 5]=>[&+5*ceil log//n&4]

Try it!

Arturo, 49 bytes

f:$->n->(n>1)?[map[2,3,4,5]=>[+1+f//n<=&]|min]->0

Try it!

Port of xnor's 50-byte Python answer.

Arturo, 71 bytes

$->n->min map[0 1 3 2 7 6 4 3 8 9 12 27 16 81 6 5]=>[&+5*ceil log//n&4]

Try it!

The formula in the OP.

Arturo, 71 bytes

$->n->min map[1 1 3 2 7 6 4 3 8 9 12 27 16 81 6 5]=>[&+5*ceil log//n&4]

Try it!

Arturo, 71 bytes

$->n->min map[0 1 3 2 7 6 4 3 8 9 12 27 16 81 6 5]=>[&+5*ceil log//n&4]

Try it!