Logarithmic equation solving

Given: $\log_2 [3 + \log_3 \{4 + \log_4 (x - 1)\}] = 2$ $3 + \log_3 \{4 + \log_4 (x - 1)\} = 2^2 = 4$ $\log_3 \{4 + \log_4 (x - 1)\} = 1$ $4 + \log_4 (x - 1) = 3^1 = 3$ $\log_4 (x - 1) = -1$ $x - 1 = 4^{-1} = \frac{1}{4}$ $x = 1 + \frac{1}{4} = \frac{5}{4}$

Therefore, $4x = 4 \times \frac{5}{4} = 5$.