詳解：等號右方將 2 併入 \(\log\)

\(2 + {\log _2}({3^x} - 2) = {\log _2}({2^2})({3^x} - 2) = {\log _2}(4 \cdot {3^x} - 8\))

\(\therefore {\log _2}({9^x} - 5) = {\log _2}(4 \cdot {3^x} - 8\))

\(\Rightarrow {9^x} - 5 = 4 \cdot {3^x} - 8\)

\(\Rightarrow {9^x} = 4 \cdot {3^x} - 3\)

\(x = 1\)