Use $\ln 6 \approx 1.7918$ , $\ln 10 \approx 2.3026$ , and the properties of logarithms to approximate $\ln \sqrt { 60 }$ to four decimal places.
A) $2.0628$
B) $16.7637$
C) $2.0472$
D) $8.1887$
E) $2.7272$

Question

Quizplus · Accepted Answer

The logarithm of the square root of 60 can be simplified using logarithm properties: $\ln \sqrt{60} = \ln (60^{1/2}) = \frac{1}{2} \ln 60$. Since $60 = 6 \times 10$, we can further simplify: $\frac{1}{2} (\ln 6 + \ln 10)$. Substituting the given values, we get $\frac{1}{2} (1.7918 + 2.3026) = \frac{1}{2} (4.0944) = 2.0472$.

Use ln⁡6≈1.7918\ln 6 \approx 1.7918ln6≈1.7918 ln⁡10≈2.3026\ln 10 \approx 2.3026ln10≈2.3026 , and the Properties of Logarithms to Approximate

Use $\ln 6 \approx 1.7918$ $\ln 10 \approx 2.3026$ , and the Properties of Logarithms to Approximate