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Question
Answer the following:
Solve for x, logx (8x – 3) – logx 4 = 2
Solution
logx (8x – 3) – logx 4 = 2
∴ `log_x ((8x - 3)/4)` = 2
∴ x2 = `(8x - 3)/4`
∴ 4x2 = 8x – 3
∴ 4x2 – 8x + 3 = 0
∴ 4x2 – 2x – 6x + 3 = 0
∴ 2x(2x – 1) – 3 (2x – 1) = 0
∴ (2x – 1) (2x – 3) = 0
∴ 2x – 1 = 0 or 2x – 3 = 0
∴ x = `1/2` or x = `3/2`
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