JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The sum of all the solutions of the equation \((8)^{2 x}-16 \cdot(8)^x+48=0\) is :
- A \(1+\log _6(8)\)
- B \(\log _8(6)\)
- C \(1+\log _8(6)\)
- D \(\log _8(4)\)
Answer & Solution
Correct Answer
(C) \(1+\log _8(6)\)
Step-by-step Solution
Detailed explanation
\( (8)^{2 x}-16 \cdot(8)^x+48=0 \) \( \text { Put } 8^x=t \) \( t^2-16+48=0 \) \( \Rightarrow t=4 \text { or } t=12 \) \( \Rightarrow 8^x=4 \quad 8^x=12 \) \( \Rightarrow x=\log _8 x \quad x=\log _8 12 \) \( \text { sum of solution }=\log _8 4+\log _8 12 \)…
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