Find the value. Give an approximation to four decimal places.
-ln(729 × 25)
A) 21.2178
B) 4.2724
C) 9.8105
D) 4.0019

Question

Quizplus · Accepted Answer

The natural logarithm of a product is equal to the sum of the natural logarithms of its factors. Thus, ln(729 × 25) = ln(729) + ln(25). Since 729 = 9^3 and 25 = 5^2, we have ln(729) = 3ln(9) and ln(25) = 2ln(5). Using a calculator, ln(9) ≈ 2.1972 and ln(5) ≈ 1.6094. Therefore, ln(729) + ln(25) ≈ 3(2.1972) + 2(1.6094) ≈ 9.8105.

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