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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2021 · Mathematics · Basics of Mathematics

If _ 10 2 _2 10+ _ 10 (10^x)=2 , then what is the value of x ?

If log⁡102log⁡210+log⁡10(10x)=2\log _{10} 2 \log _2 10+\log _{10}\left(10^x\right)=2, then what is the value of xx ?

Options

  1. A0
  2. B1
  3. Clog⁡210\log _2 10
  4. Dlog⁡52\log _5 2

Correct answer

B. 1

Step-by-step solution

log⁡102log⁡210+log⁡10(10x)=2⇒log⁡1010+xlog⁡1010=2[∴log⁡ba×log⁡ac=log⁡bc]⇒1+x=2⇒x=1[∴log⁡1010=1]\begin{aligned} & \log _{10} 2 \log _2{ }^{10}+\log _{10}\left(10^x\right)=2 \\ & \Rightarrow \log _{10} 10+x \log _{10} 10=2\left[\therefore \log _b{ }^a \times \log _a{ }^c=\log _b c\right] \\ & \Rightarrow 1+x=2 \\ & \Rightarrow x=1\left[\therefore \log _{10} 10=1\right]\end{aligned}
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