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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Main · Mathematics · Basics of Mathematics

If a, b, c, ≠ 0 and belong to the set to \ 0,1,2, 3 , 9\ , then _...

If a,b,c,≠0a, b, c, \neq 0 and belong to the set to {0,1,2,3……,9}\{0,1,2, 3 \ldots \ldots, 9\}, then log⁡10(a+10b+102c10−4a+10−3b+10−2c)isequalto\log _{10} \left(\frac{a+10 b+10^2 c}{10^{-4} a+10^{-3} b+10^{-2} c}\right)is equal to

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

D. 4

Step-by-step solution

log⁡10(a+10b+102c10−4a+10−3b+10−2c)=log⁡10(a+10b+102c1104(a+10b+102c))=log⁡10104=4\begin{aligned} & \log _{10}\left(\frac{a+10 b+10^2 c}{10^{-4} a+10^{-3} b+10^{-2} c}\right) \\ & =\log _{10}\left(\frac{a+10 b+10^2 c}{\frac{1}{10^4}\left(a+10 b+10^2 c\right)}\right)=\log _{10} 10^4=4\end{aligned}
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