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1967 AMC 12 Question 26

AMC12 · 1967 AMC 12

Question 26

If one uses only the tabular information $10^3=1000,$ $10^4=10{,}000,$ $2^{10}=1024,$ $2^{11}=2048,$ $2^{12}=4096,$ $2^{13}=8192,$ then the strongest statement one can make for $\log_{10}2$ is that it lies between:
  1. $\dfrac3{10}$ and $\dfrac4{11}$
  2. $\dfrac3{10}$ and $\dfrac4{12}$
  3. $\dfrac3{10}$ and $\dfrac4{13}$
  4. $\dfrac3{10}$ and $\dfrac{40}{132}$
  5. $\dfrac3{11}$ and $\dfrac{40}{132}$