Correct option is (3) \(1+\log _{8}(6)\)
\((8)^{2 \mathrm{x}}-16 \cdot(8)^{\mathrm{x}}+48=0\)
Put \(8^{\mathrm{x}}=\mathrm{t}\)
\(\mathrm{t}^{2}-16+48=0\)
\(\Rightarrow \mathrm{t}=4\) or \(\mathrm{t}=12\)
\(\Rightarrow 8^{\mathrm{x}}=4 \quad 8^{\mathrm{x}}=12\)
\(\Rightarrow \mathrm{x}=\log _{8} \mathrm{x} \quad \mathrm{x}=\log _{8} 12\)
sum of solution \(=\log _{8} 4+\log _{8} 12\)
\(=\log _{8} 48=\log _{8}(6.8)\)
\(=1+\log _{8} 6\)
