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Let N = (0.7214 x 20.37)/(608). Take the logarithm of both sides.

Mathematics

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Question 11: Use logarithms table to evaluate: 0.7214×20.37608\frac{0.7214 \times 20.37}{608}

  1. Let N=0.7214×20.37608N = \frac{0.7214 \times 20.37}{608}.

    Take the logarithm of both sides.

    log⁡N=log⁡(0.7214)+log⁡(20.37)−log⁡(608)\log N = \log(0.7214) + \log(20.37) - \log(608)
  2. Find the logarithms of each number using logarithm tables.

    log⁡(0.7214)=1ˉ.8582\log(0.7214) = \bar{1}.8582 log⁡(20.37)=1.3090\log(20.37) = 1.3090 log⁡(608)=2.7839\log(608) = 2.7839
  3. Perform the addition and subtraction of the logarithms.

    log⁡N=1ˉ.8582+1.3090−2.7839\log N = \bar{1}.8582 + 1.3090 - 2.7839

    First, add the positive logarithms:

    1ˉ.8582+1.3090=(−1+0.8582)+(1+0.3090)=0.8582+0.3090=1.1672\bar{1}.8582 + 1.3090 = (-1 + 0.8582) + (1 + 0.3090) = 0.8582 + 0.3090 = 1.1672

    Now, subtract the logarithm of the denominator:

    log⁡N=1.1672−2.7839\log N = 1.1672 - 2.7839 log⁡N=−1.6167\log N = -1.6167
  4. Convert the negative logarithm to the standard characteristic-mantissa form.

    −1.6167=−2+0.3833=2ˉ.3833-1.6167 = -2 + 0.3833 = \bar{2}.3833
  5. Find

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