Question
Download Solution PDFIf log (x + 2) + log (x − 2) = log 5 then the value of x will be
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Logarithm properties
Product rule: The log of a product equals the sum of two logs.
Quotient rule: The log of a quotient equals the difference of two logs.
Calculation:
Given:
log (x + 2) + log (x − 2) = log 5
⇒ log [(x + 2) (x – 2)] = log 5 (∵
⇒ log (x 2 – 4) = log 5
⇒ x2 – 4 = 5
⇒ x2 = 9
∴ x = ± 3
Here x ≠ -3 is not possible because (x – 2) should be greater than zero.
∴ x = 3
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