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Given Log (log x) + Log ( Log x³ - 2 ) = 0 => Log [ (log x) (3 Log x - 2) ] = 0 => (Log x ) * (3 Log x - 2) = 1

As we have Log (log x) defined, log x is positive.

Let Log x = z, So we have

z * (3 z - 2) = 1 3 z² - 2 z - 1 = 0 The factors of 3*-1 are -3 and +1, and their sum is -2. (3z + 1) (z - 1) = 0

So z = -1/3 or z = 1. we ignore the negative value, for the reason mentioned above. So Log x = 1 => x = 10.