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Evaluate 2(0.125).

Mathematics

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Answer

B

Step-by-step solution

3 steps

Here are the solutions to the problems:

13. Evaluate log⁡2(0.125)\log_2(0.125).

  1. Convert the decimal to a fraction.

    0.125=1251000=180.125 = \frac{125}{1000} = \frac{1}{8}

  2. Express the fraction as a power of 2.

    18=123=2−3\frac{1}{8} = \frac{1}{2^3} = 2^{-3}

  3. Substitute this into the logarithm and use the property log⁡b(bx)=x\log_b(b^x) = x.

    log⁡2(0.125)=log⁡2(2−3)=−3\log_2(0.125) = \log_2(2^{-3}) = -3

    The correct option is B

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