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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2019 · Mathematics · Basics of Mathematics

If f(x)= _ 10 (1+x) , then what is 4 f(4)+5 f(1)- _ 10 2 equal to?

If f(x)=log⁡10(1+x)f(x)=\log _{10}(1+x), then what is 4f(4)+5f(1)−log⁡1024 f(4)+5 f(1)-\log _{10} 2 equal to?

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

f(x)=log⁡10(1+x)f(x)=\log _{10}(1+x)4⋅f(4)+5⋅f(1)−log⁡102=4⋅log⁡10(1+4)+5⋅log⁡10(1+1)−log⁡102=4log⁡105+5log⁡102−log⁡102=4log⁡105+4log⁡102=4(log⁡105+log⁡102)=4(log⁡1010)=4\begin{aligned} & 4 \cdot f(4)+5 \cdot f(1)-\log _{10} 2 \\ & =4 \cdot \log _{10}(1+4)+5 \cdot \log _{10}(1+1)-\log _{10} 2 \\ & =4 \log _{10} 5+5 \log _{10} 2-\log _{10} 2 \\ & =4 \log _{10} 5+4 \log _{10} 2 \\ & =4\left(\log _{10} 5+\log _{10} 2\right) \\ & =4\left(\log _{10} 10\right)=4\end{aligned}$$
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