Multiple choice

If (\log 2 = 0.3010) and (\log 3 = 0.4771), then find the approximate value of (\log 36).

  1. 2.65

  2. 1.65

  3. 1.56

  4. 2.56

  5. 3.02
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C Correct answer
Explanation

log(36) = log(6^2) = 2*log(6) = 2*(log(2) + log(3)) = 2*(0.3010 + 0.4771) = 2*(0.7781) = 1.5562, which is approximately 1.56.

AI explanation

Using the power and product properties of logarithms, log 36 equals log(6^2), which simplifies to 2 log(6). Applying the product rule again, 2 log(2 times 3) yields 2(log 2 + log 3). Substituting the values gives 2(0.3010 + 0.4771), which equals 2(0.7781) or 1.5562. Rounding to two decimal places, the value is 1.56.

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