Very hard and challenging logarithmic problem?

Question

I don't know how to do it and I am stumped.

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Answer 1 · 2017-02-27T17:10:45

See below.

The biggest consistent set of equations is

${(), (log(1.5) = 2 b - 2), (log(0.\bar 6)= 2 - 2 b), (log(6) = 2 a), (log(8) = 3 a - 3 b + 3), (log(9) = 2 a + 2 b - 2), () :}$

For this set of equations we have

$a=log(6)/2$ and $b = 1+log(3/2)/2$