# Bowers' Arrays IV

Number Theory Level pending

For this problem, $${ log }_{ 3 }^{ x }(n)$$ denotes the repeated $$log_{ 3 }$$. For example, $${ log }_{ 3 }^{ 2 }(n)$$ represents $${ log }_{ 3 }({ log }_{ 3 }(n))$$.

With that in mind, what is the sum of $$a$$ and $$b$$ in the equation for $$x$$ so that $${ log }_{ 3 }^{ x }(\{ 3,n,2\} )$$ returns a decimal number with fewer than ten digits, when the equation is written in the form $$x = an + b$$?

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