# Very hard and challenging logarithmic problem?

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

Feb 27, 2017

See below.

#### Explanation:

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

$a = \log \frac{6}{2}$ and $b = 1 + \log \frac{\frac{3}{2}}{2}$