Find the value of x, if log5 (x - 2) + log5 (x + 3) = log5 14.1. 22. 3

1.	Find the value of x, if log5 (x - 2) + log5 (x + 3) = log5 14.1. 22. 33. 44. 5
Answer» Correct Answer - Option 3 : 4 CONCEPT: Logarithmic product rule is represented as log_p (x) + log _p(y) = log_p(x.y) Log is not defined for negative values. CALCULATION: Given that log₅ (x - 2) + log₅ (x + 3) = log₅ 14 Dropping log from the both sides we get- ⇒ (x - 2) × (x + 3) = 14 ⇒x² + x - 6 = 14 ⇒ x² + x - 20 = 0 On solving the quadratic equation x² + x - 20 = 0 ⇒ (x - 4) × (x + 5) = 0 ⇒ x = 4 and x = - 5 Therefore x = 4. (negative value of x will be excluded) Therefore, option (3) is the correct answer.

Find the value of x, if log5 (x - 2) + log5 (x + 3) = log5 14.1. 22. 33. 44. 5

Answer» Correct Answer - Option 3 : 4

CONCEPT:

Logarithmic product rule is represented as log_p (x) + log _p(y) = log_p(x.y)
Log is not defined for negative values.

CALCULATION:

Given that log₅ (x - 2) + log₅ (x + 3) = log₅ 14

Dropping log from the both sides we get-

⇒ (x - 2) × (x + 3) = 14

⇒x² + x - 6 = 14

⇒ x² + x - 20 = 0

On solving the quadratic equation

x² + x - 20 = 0

⇒ (x - 4) × (x + 5) = 0

⇒ x = 4 and x = - 5

Therefore x = 4. (negative value of x will be excluded)

Therefore, option (3) is the correct answer.

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Find the value of x, if log5 (x - 2) + log5 (x + 3) = log5 14.1. 22. 33. 44. 5

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