If p = log₁₀ 20 and q = log₁₀ 25, find the value of x if
2log₁₀ (x + 1) = 2p - q

Question

If p = log₁₀ 20 and q = log₁₀ 25, find the value of x if 2log₁₀ (x + 1) = 2p - q

KnowledgeBoat · Accepted Answer

Given, 2log₁₀(x + 1) = 2p - q ⇒ 2log₁₀(x + 1) = 2log₁₀20 - log₁₀25 ⇒ log₁₀(x + 1)² = log₁₀20² - log₁₀25 ⇒ log₁₀(x + 1)² = log₁₀400 - log₁₀25 ⇒ log₁₀(x + 1)² = ⇒ log₁₀(x + 1)² = log₁₀16 ⇒ (x + 1)² = 16 ⇒ x² + 1 + 2x = 16 x² + 2x - 15 = 0 x² + 5x - 3x - 15 = 0 x(x + 5) - 3(x + 5) = 0 (x - 3)(x + 5) = 0 x = 3 or -5. But x ≠ -5 as then (x + 1) will be negative. Hence, x = 3.

Mathematics

If p = log₁₀ 20 and q = log₁₀ 25, find the value of x if
2log₁₀ (x + 1) = 2p - q

Logarithms

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If p = log10 20 and q = log10 25, find the value of x if2log10 (x + 1) = 2p - q

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If p = log₁₀ 20 and q = log₁₀ 25, find the value of x if
2log₁₀ (x + 1) = 2p - q