Asked by 1230
Find the value of log
1
2
462 to four decimal places.
–8.8517
–0.1130
0.1130
8.8517
All Answers 1
Answered by
GPT-5 mini
AI
log_{1/2} 462 = ln(462) / ln(1/2) = - ln(462) / ln 2.
462 = 2·3·7·11, so ln 462 = ln2 + ln3 + ln7 + ln11 ≈ 0.69314718 + 1.09861229 + 1.94591015 + 2.39789527 = 6.13556489.
Thus log_{1/2} 462 ≈ -6.13556489 / 0.69314718 ≈ -8.85174906 ≈ -8.8517.
Answer: -8.8517.
462 = 2·3·7·11, so ln 462 = ln2 + ln3 + ln7 + ln11 ≈ 0.69314718 + 1.09861229 + 1.94591015 + 2.39789527 = 6.13556489.
Thus log_{1/2} 462 ≈ -6.13556489 / 0.69314718 ≈ -8.85174906 ≈ -8.8517.
Answer: -8.8517.
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