Question
Download Solution PDFlog (x + 3) + log (x + 5) = log 35, x విలువను కనుగొనండి?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇవ్వబడింది:
log (x + 3) + log (x + 5) = log 35
ఉపయోగించిన సూత్రం:
log a + log b = log (a × b)
log a = log b, అయితే, a = b
గణన:
లాగరిథం ప్రాపర్టీ log a + log b = log (a × b) ఉపయోగించి:
log [(x + 3)(x + 5)] = log 35
రెండు వైపులా లాగరిథమ్లు సమానంగా ఉంటాయి కాబట్టి, వాటి వాదనలు సమానంగా ఉండాలి:
(x + 3)(x + 5) = 35
x2 + 5x + 3x + 15 = 35
x2 + 8x + 15 - 35 = 0
x2 + 8x - 20 = 0
(x + 10)(x - 2) = 0
x + 10 = 0 ⇒ x = -10
x - 2 = 0 ⇒ x = 2
రుణాత్మక సంఖ్య యొక్క లాగరిథం నిర్వచించబడలేదు.
కాబట్టి, x = 2 ఒక చెల్లుబాటు అయ్యే విలువ.
∴ x విలువ 2.
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