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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2018 · Mathematics · Basics of Mathematics

If (0.2)^x=2 and _ 10 2=0.3010 , then what is the value of x to the...

If (0.2)x=2(0.2)^x=2 and log⁡102=0.3010\log _{10} 2=0.3010, then what is the value of xx to the nearest tenth?

Options

  1. A-10.0
  2. B-0.5
  3. C-0.4
  4. D-0.2

Correct answer

C. -0.4

Step-by-step solution

(0.2)x=2(0.2)^x=2 Taking log⁡\log on both sides, xlog⁡10210=log⁡102x[log⁡102−log⁡1010]=log⁡102x[0.3010−1]=0.3010x=−0.30100.6990≈−0.43\begin{aligned} & x \log _{10} \frac{2}{10}=\log _{10} 2 \\ & x\left[\log _{10} 2-\log _{10} 10\right]=\log _{10} 2 \\ & x[0.3010-1]=0.3010 \\ & x=-\frac{0.3010}{0.6990} \approx-0.43 \end{aligned}
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