2023
Mathematics
67ca00ce0c643c71d77dee1f
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: y = ±17
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 (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
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 = ±17THIS WEEK's
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