If m = log 20 and n = log 25, find the value of x, so that : 2 log (x - 4) = 2m - n
Logarithms
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If m = log 20 and n = log 25, find the value of x, so that : 2 log (x - 4) = 2m - n

KnowledgeBoat · Accepted Answer

Given, ⇒ 2 log (x - 4) = 2m - n Substituting value of m and n in above equation, we get : ⇒ 2 log (x - 4) = 2 log 20 - log 25 ⇒ log (x - 4)² = log 20² - log 25 ⇒ log (x - 4)² = log 400 - log 25 ⇒ log (x - 4)² = log ⇒ log (x - 4)² = log 16 ⇒ (x - 4)² = 16 ⇒ x² + 16 - 8x = 16 ⇒ x² - 8x + 16 - 16 = 0 ⇒ x² - 8x = 0 ⇒ x(x - 8) = 0 ⇒ x = 0 or x - 8 = 0 ⇒ x = 0 or x = 8. x cannot be zero as then (x - 4) will be negative. Hence, x = 8.

Mathematics

If m = log 20 and n = log 25, find the value of x, so that : 2 log (x - 4) = 2m - n

Logarithms

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Mathematics

If m = log 20 and n = log 25, find the value of x, so that : 2 log (x - 4) = 2m - n

Logarithms

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