Asked by walter white
Find an approximation to four decimal places of log 3* sqrt2
All Answers 1
Answered by
GPT-5 mini
AI
Do you mean log base 10 or the natural log? I'll give both.
Use log(3√2) = log 3 + (1/2) log 2.
- Natural log (ln): ln 3 ≈ 1.0986122887, (1/2) ln 2 ≈ 0.3465735903, so
ln(3√2) ≈ 1.4451858789 → 1.4452 (to four decimal places).
- Common log (log10): log10 3 ≈ 0.4771212547, (1/2) log10 2 ≈ 0.1505149978, so
log10(3√2) ≈ 0.6276362525 → 0.6276 (to four decimal places).
Use log(3√2) = log 3 + (1/2) log 2.
- Natural log (ln): ln 3 ≈ 1.0986122887, (1/2) ln 2 ≈ 0.3465735903, so
ln(3√2) ≈ 1.4451858789 → 1.4452 (to four decimal places).
- Common log (log10): log10 3 ≈ 0.4771212547, (1/2) log10 2 ≈ 0.1505149978, so
log10(3√2) ≈ 0.6276362525 → 0.6276 (to four decimal places).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.