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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2013 · Mathematics · Basics of Mathematics

What is _ 81 243 equal to?

What is log⁡81243\log _{81} 243 equal to?

Options

  1. A0.75
  2. B1.25
  3. C1.5
  4. D3

Correct answer

B. 1.25

Step-by-step solution

log⁡81243=log⁡(3)4(3)5\log _{81} 243=\log _{(3)^4}(3)^5 From Log properties, log⁡(b)y(a)x=xylog⁡ba\log _{(b)^y}(a)^x=\frac{x}{y} \log _b a Similarly, log⁡(3)4(3)5=54log⁡33=54=1.25\begin{aligned} \log _{(3)^4}(3)^5 & =\frac{5}{4} \log _3 3 \\ & =\frac{5}{4}=1.25 \end{aligned}
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