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If log125729 = x, then what is the value of log815625?1. 2x/(4 - x)2. (4 - x)/2x3. (4 + x)/2x4. 2x/(4 + x) |
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Answer» Correct Answer - Option 3 : (4 + x)/2x Calculation: log125729 = x ⇒ loga729/loga125 = x ⇒ loga(9)3/loga(5)3= x ⇒ 3loga9/3loga5= x ⇒ loga9/loga5 = x ⇒ log59=x ⇒ log95 = 1/x ⇒ log35 = 2/x Now, log815625 ⇒ log81(625× 9) ⇒ log81625 + log819 ⇒ log(3)4(5)4+ log(9)2(9) ⇒ log35 + 1/2 ⇒ 2/x + 1/2 ⇒ (4 + x)/2x The value of log815625 is (4 + x)/2x. loga(MN) = logaM + logaN logMN = logaN/ logaM loga(M)b= b× logaM loga(a) = 1 If loga(b) = x then, logb(a) = 1/x |
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