The sum of all the solutions of the equation | vedclass

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Question

$ (8)^{2 x}-16 \cdot(8)^x+48=0 $

$ 	ext { Put } 8^x=t $

$ t^2-16+48=0 $

$ \Rightarrow t=4 	ext { or } t=12 $

$ \Rightarrow 8^x=4 \quad 8

Vedclass · Accepted Answer

$1+\log _8(6)$

Vedclass · Answer

$ (8)^{2 x}-16 \cdot(8)^x+48=0 $

$ 	ext { Put } 8^x=t $

$ t^2-16+48=0 $

$ \Rightarrow t=4 	ext { or } t=12 $

$ \Rightarrow 8^x=4 \quad 8^x=12 $

$ \Rightarrow x=\log _8 x \quad x=\log _8 12 $

$ 	ext { sum of solution }=\log _8 4+\log _8 12 $

$ =\log _8 48=\log _8(6.8) $

$ =1+\log _8 6$

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

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