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The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is :
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Verified Answer
The correct answer is:
$1+\log _8(6)$
$\begin{aligned} & (8)^{2 x}-16 \cdot(8)^x+48=0 \\ & \text { Put } 8^{\mathrm{x}}=\mathrm{t} \\ & \mathrm{t}^2-16+48=0 \\ & \Rightarrow \mathrm{t}=4 \text { or } \mathrm{t}=12 \\ & \Rightarrow 8^x=4 \quad 8^x=12 \\ & \Rightarrow \mathrm{x}=\log _8 \mathrm{x} \quad \mathrm{x}=\log _8 12 \\ & \end{aligned}$
sum of solution $=\log _8 4+\log _8 12$
$\begin{aligned} & =\log _8 48=\log _8(6.8) \\ & =1+\log _8 6\end{aligned}$
sum of solution $=\log _8 4+\log _8 12$
$\begin{aligned} & =\log _8 48=\log _8(6.8) \\ & =1+\log _8 6\end{aligned}$
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