Find the value of y, if log (y + 8) + log (y – 8) = 2log 3 + 2log 5
- y = ±5
- y = ±10
-
y = ±17
- y = ±13
The correct answer is: C
Explanation
log (y + 8) + log (y - 8) = 2log 3 + 2log 5
⇒ log (y + 8)(y - 8) = 2log 3 + 2log 5 (log ab = log a + log b)
⇒ log (y\(^2\) -8y + 8y - 64) = log 3\(^2\) + log 5\(^2\)
⇒ log (y\(^2\) - 64) = log 3\(^2\) + log 5\(^2\)
⇒ log (y\(^2\) - 64) = log 9 + log 25
⇒ log (y\(^2\) - 64) = log (9 × 25)
⇒ log(y\(^2\) - 64) = log 225
⇒ y\(^2\) - 64 = 225
⇒ y\(^2\) = 225 + 64
⇒ y\(^2\) = 289
⇒ y = ±√289
∴ y = ±17
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