If p = log 20 and q = log 25, find the value of x, if 2 log (x + 1) = 2p - q.

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KnowledgeBoat · Accepted Answer

Given, ⇒ 2 log (x + 1) = 2p - q Substituting value of p and q in above equation, we get : ⇒ 2 log (x + 1) = 2 log 20 - log 25 ⇒ log (x + 1)² = log 20² - log 25 ⇒ log (x + 1)² = log 400 - log 25 ⇒ log (x + 1)² = log ⇒ log (x + 1)² = log 16 ⇒ (x + 1)² = 16 ⇒ x² + 1 + 2x = 16 ⇒ x² + 2x + 1 - 16 = 0 ⇒ x² + 2x - 15 = 0 ⇒ x² + 5x - 3x - 15 = 0 ⇒ x(x + 5) - 3(x + 5) = 0 ⇒ (x - 3)(x + 5) = 0 ⇒ x - 3 = 0 or x + 5 = 0 ⇒ x = 3 or x = -5. But x cannot be negative, then x + 1 will be negative which is not possible. Hence, x = 3.

Mathematics

If p = log 20 and q = log 25, find the value of x, if 2 log (x + 1) = 2p - q.

Logarithms

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Mathematics

If p = log 20 and q = log 25, find the value of x, if 2 log (x + 1) = 2p - q.

Logarithms

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