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If log8 9, log8 (2y+7) and log8 (3y+6) are in arithmetic progression with non-zero common difference, find the value of y.
If log8 9, log8 (2y+7) and log8 (3y+6) are in arithmetic progression with non-zero common difference, find the value of y.
Updated On: Aug 31, 2024
- 1
- 2.25
- –1.25
- 1.25
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The Correct Option is C
Solution and Explanation
log8 9, log8 (2y + 7) and log8 (3y + 6) are in arithmetic progression
So, 2log8 (2y + 7) = log8 9 + log8 (3y + 6)
log8 (2y + 7)2 = log8 (27y + 54)
(2y + 7)2 = (27y + 54)
4y2 + 49 + 28y = 27y + 54
4y2 + y – 5 = 0
4y2 – 4y + 5y – 5 = 0
4y(y – 1) + 5(y – 1) = 0
y = 1 or y = – 1.25
Since, the common difference is non-zero, so, y= – 1.25.
So the correct option is (C) : -1.25.
So, 2log8 (2y + 7) = log8 9 + log8 (3y + 6)
log8 (2y + 7)2 = log8 (27y + 54)
(2y + 7)2 = (27y + 54)
4y2 + 49 + 28y = 27y + 54
4y2 + y – 5 = 0
4y2 – 4y + 5y – 5 = 0
4y(y – 1) + 5(y – 1) = 0
y = 1 or y = – 1.25
Since, the common difference is non-zero, so, y= – 1.25.
So the correct option is (C) : -1.25.
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