Given 2 log₁₀ x + 1 = log₁₀ 250, find : (i) x (ii) log₁₀ 2x

Question

KnowledgeBoat · Accepted Answer

(i) Given, ⇒ 2 log₁₀ x + 1 = log₁₀ 250 ⇒ log₁₀ x² + log₁₀ 10 = log₁₀ 250 ⇒ log₁₀ (x² × 10) = log₁₀ 250 ⇒ log₁₀ (10x²) = log₁₀ 250 ⇒ 10x² = 250 ⇒ x² = ⇒ x² = 25 ⇒ x = = 5. Hence, x = 5. (ii) Substituting value of x in log₁₀ 2x, we get : ⇒ log₁₀ 2x ⇒ log₁₀ 2(5) ⇒ log₁₀ 10 ⇒ 1. Hence, log₁₀ 2x = 1.

Mathematics

Given 2 log₁₀ x + 1 = log₁₀ 250, find :
(i) x
(ii) log₁₀ 2x

Logarithms

Related Questions

If log 2 = 0.3010 and log 3 = 0.4771; find the value of log 25.

If log₂ (log₃ x) = 4, the value of x is :
3¹⁶
16³
3 × 16
16 ÷ 3