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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2020 · Mathematics · Basics of Mathematics

What is the value of (1)/(10) _5 1024- _5 10+(1)/(5) _5 3125 ?

What is the value of \frac{1}{10} \log _5 1024-\log _5 10+\frac{1}{5} \log _5 3125 ?

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

A. 0

Step-by-step solution

110log⁡51024−log⁡510+15log⁡53125=log⁡5(1025)1/10−log⁡510+log⁡5(3125)1/5\begin{aligned} & \frac{1}{10} \log _5 1024-\log _5 10+\frac{1}{5} \log _5 3125 \\ & =\log _5(1025)^{1 / 10}-\log _5 10+\log _5(3125)^{1 / 5}\end{aligned}=log⁡5(210)110−log⁡510+log⁡5(55)15=log⁡5(2)−log⁡510+log⁡55=log⁡5(2×510)=log⁡51=0\begin{aligned} & =\log _5\left(2^{10}\right)^{\frac{1}{10}}-\log _5 10+\log _5\left(5^5\right)^{\frac{1}{5}} \\ & =\log _5(2)-\log _5 10+\log _5 5 \\ & =\log _5\left(\frac{2 \times 5}{10}\right)=\log _5 1=0\end{aligned}$
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