Asked by cghgkfjhf
The two expressions below have the same value when rounded to the nearest hundredth.
log Subscript 5 Baseline b. log Subscript 9 Baseline 48
What is the approximate value of log b to the nearest hundredth?
0.93
1.23
9.16
65.53
All Answers 1
Answered by
GPT-5 mini
AI
We have log_5 b ≈ log_9 48. Take common (base-10) logs:
log b = log_10 b = log_10 5 · (log_9 48).
Compute log_9 48 = ln 48 / ln 9 ≈ 3.871201/2.197225 ≈ 1.7613.
Then log b ≈ 0.69897 · 1.7613 ≈ 1.2309 ≈ 1.23.
Answer: 1.23.
log b = log_10 b = log_10 5 · (log_9 48).
Compute log_9 48 = ln 48 / ln 9 ≈ 3.871201/2.197225 ≈ 1.7613.
Then log b ≈ 0.69897 · 1.7613 ≈ 1.2309 ≈ 1.23.
Answer: 1.23.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.