Can we solve these three simultaneous log equations?

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Three positive numbers \(a\), \(b\), \(c\) satisfy \[\log_b a = 2, \qquad \log_b (c-3) = 3, \qquad \log_a (c+5) = 2.\] This information

1. specifies \(a\) uniquely.

2. is satisfied by two values of \(a\).

3. is satisfied by infinitely many values of \(a\).

4. is contradictory.