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Find the value of y, if log (y + 8) + log (y - 8) = 2log ...

Find the value of y, if log (y + 8) + log (y - 8) = 2log 3 + 2log 5

A.

y = ±5

B.

y = ±10

C.

y = ±17

D.

y = ±13

Correct answer is C

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 (y2 -8y + 8y - 64) = log 32 + log 52

⇒ log (y2 - 64) = log 32 + log 52

⇒ log (y2 - 64) = log 9 + log 25

⇒ log (y2 - 64) = log (9 × 25)

⇒ log(y2 - 64) = log 225

⇒ y2 - 64 = 225

⇒ y2 = 225 + 64

⇒ y2 = 289

⇒ y = ±√289

∴ y = ±17