Correct Answer: Option 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

There is an explanation video available below.

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