Transform the dataset[100, 200, 1000] using the logarithmic transformationf(x)=log10(x). What is the transformed dataset?

Question

Transform the dataset[100, 200, 1000] using the logarithmic transformationf(x)=log10​(x). What is the transformed dataset?

BlackTom AI · Accepted Answer

log10(100) = 2, so the transformed values follow directly from base‑10 logarithm properties.

1) Relevant knowledge points and concepts
- log10(x) gives the power to which 10 must be raised to get x.
- log10(ab) = log10(a) + log10(b); this helps compute log10(200) by factoring 200 = 2 × 100.
- Exact powers of 10 have integer logs: log10(100) = 2, log10(1000) = 3.

2) Step‑by‑step reasoning
Apply f(x) = log10(x) to each element of the dataset [100, 200, 1000].

3) Calculations with intermediate steps
- For x = 100: log10(100) = log10(10^2) = 2.
- For x = 200: write 200 = 2 × 100, so
  log10(200) = log10(2 × 100) = log10(2) + log10(100) = log10(2) + 2.
  Using the common logarithm value log10(2) ≈ 0.30103, we get log10(200) ≈ 0.30103 + 2 = 2.30103, which rounds to 2.3 (to two significant figures or one decimal place as shown in the choices).
- For x = 1000: log10(1000) = log10(10^3) = 3.

4) Why the correct answer is correct
The transformed dataset is therefore [2, 2.30103..., 3]. The multiple‑choice option approximates the middle value as 2.3, so the correct choice is [2, 2.3, 3].

5) Why the other options are incorrect
- a. [0, 1, 2] would be log10([1, 10, 100]) not our input values.
- c. [10, 100, 1000] are the original numbers or would be 10× larger than the inputs; they are not logarithms.
- d. [1, 2, 3] corresponds to log10([10, 100, 1000]) — only the second and third match our logs, but the first does not.

6) Conclusion
The transformed dataset is [2, 2.3, 3], which matches option b.

Transform the dataset[100, 200, 1000] using the logarithmic transformationf(x)=log10(x). What is the transformed dataset?单项选择题

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Transform the dataset[100, 200, 1000] using the logarithmic transformationf(x)=log10​(x). What is the transformed dataset?单项选择题