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Let $0.01^x+0.25^x=0.7$ . Then

  1. $x\geq1$
  2. $0\lt x\lt1$
  3. $x\leq0$
  4. no such real number $x$ is possible.
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1 Answer

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$\underline{\mathbf{Answer:B}}\;$ $\bbox[orange,5px,border: 2px dotted red]{\color{blue}{\mathbf{0<x<1}}}$

$\underline{\mathbf{Explanation:}}$

Substitute $\mathbf {x = 0} \Rightarrow (0.001)^0 + (0.25)^0 = 1 + 1 = 2 \;\text{which is }\; \color{red}{> 0.7}$

Similarly, subsitute $\mathbf {x = 1} \Rightarrow (0.01)^1 + (0.25)^1 = 0.26\;\text{which is }\; \color{red}{< 0.7}$

$\therefore \mathbf x$ lies between $\mathbf 0$ and $\mathbf 1$.

$\therefore \mathbf B$ is the right option.
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