Question:

The sum of all the solutions of the equation $(8)^{2x}-16\cdot(8)^x+48=0$ is:

$1+\log_8(6)$

$1+\log_6(8)$

$\log_8(6)$

$\log_8(4)$

Step-by-Step Solution

Key Concept: Let $t=8^x$: $t^2-16t+48=0\Rightarrow t=4$ or $t=12$. So $8^x=4\Rightarrow x=\log_8 4$ and $8^x=12\Rightarrow x=\log_8 12$.

Sum $=\log_8 48=1+\log_8 6$.

Correct Answer: 1