Find the domain of function `f(x)=(log)_4[(log)_5{(log)_3(18 x-x^2-77}]`

Explanation

To find the domain of the function \( f(x) = \log_4 \left( \log_5 \left( \log_3 (18x - x^2 - 77) \right) \right) \), we need to ensure that all logarithmic expressions are defined and positive.

### Step 1: Find the innermost logarithm condition
The innermost function is \( \log_3(18x - x^2 - 77) \). For this logarithm to be defined, the argument must be greater than 0:
\[ 18x - x^2 - 77 > 0 \]
Rearranging gives:
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