1.

If log125729 = x, then what is the value of log815625?1. 2x/(4 - x)2. (4 - x)/2x3. (4 + x)/2x4. 2x/(4 + x)

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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