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

Question

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

Krishna Veeni · Accepted Answer

Final Answer : C, Explanation :   The logarithm of the square root of 60 can be simplified using logarithm properties:   ln ⁡ 60 = ln ⁡ ( 6 0 1 / 2 ) = 1 2 ln ⁡ 60 \ln \sqrt{60} = \ln (60^{1/2}) = \frac{1}{2} \ln 60 ln 60 ​ = ln ( 6 0 1/2 ) = 2 1 ​ ln 60  . Since   60 = 6 × 10 60 = 6 	imes 10 60 = 6 × 10  , we can further simplify:   1 2 ( ln ⁡ 6 + ln ⁡ 10 ) \frac{1}{2} (\ln 6 + \ln 10) 2 1 ​ ( ln 6 + ln 10 )  . Substituting the given values, we get   1 2 ( 1.7918 + 2.3026 ) = 1 2 ( 4.0944 ) = 2.0472 \frac{1}{2} (1.7918 + 2.3026) = \frac{1}{2} (4.0944) = 2.0472 2 1 ​ ( 1.7918 + 2.3026 ) = 2 1 ​ ( 4.0944 ) = 2.0472  .

Use $ln⁡6≈1.7918\ln 6 \approx 1.7918$ , $ln⁡10≈2.3026\ln 10 \approx 2.3026$ , and the properties of logarithms to approximate $ln⁡60\ln \sqrt { 60 }$ to four decimal places.

A) $2.0628$
B) $16.7637$
C) $2.0472$
D) $8.1887$
E) $2.7272$

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