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Expand a logarithm using the log laws

11th grade (Year 12 in England) · 16 questions · Common Core: HSF.LE.A.4 · England: A-level Pure Mathematics

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1
Question 1
Felix says log(x³) = (log x)³. Which is the correct rewrite of log(x³)?
- A. log x ÷ 3
- B. (log x)³
- C. log 3 + log x
- D. 3 log x
2
Question 2
a = log x, b = log y and c = log z. Write log(xy³/z) in terms of a, b and c.
- A. 4a − c
- B. a × 3b ÷ c
- C. a + 3b − c
- D. a3b − c
3
Question 3
Priya says log(x⁵) = (log x)⁵. Which is the correct rewrite of log(x⁵)?
- A. 5 log x
- B. (log x)⁵
- C. log x ÷ 5
- D. log 5 + log x
4
Question 4
a = log x, b = log y and c = log z. Write log(x³y/z) in terms of a, b and c.
- A. 3a + b + c
- B. 3a + b − c
- C. 3ab − c
- D. 3a × b ÷ c
5
Question 5
Ana says log(x⁴) = (log x)⁴. Which is the correct rewrite of log(x⁴)?
- A. log x ÷ 4
- B. 4 log x
- C. log 4 + log x
- D. (log x)⁴
6
Question 6
a = log x, b = log y and c = log z. Write log(xy²/z²) in terms of a, b and c.
- A. 3a − 2c
- B. a + 2b + 2c
- C. a × 2b ÷ 2c
- D. a + 2b − 2c
7
Question 7
Elena says log(x³) = (log x)³. Which is the correct rewrite of log(x³)?
- A. log 3 + log x
- B. log x ÷ 3
- C. (log x)³
- D. 3 log x
8
Question 8
a = log x, b = log y and c = log z. Write log(x⁴y²/z²) in terms of a, b and c.
- A. 4a + 2b + 2c
- B. 4a × 2b ÷ 2c
- C. 4a2b − 2c
- D. 4a + 2b − 2c
9
Question 9
Sofia says log(x⁵) = (log x)⁵. Which is the correct rewrite of log(x⁵)?
- A. (log x)⁵
- B. log x ÷ 5
- C. 5 log x
- D. log 5 + log x
10
Question 10
a = log x, b = log y and c = log z. Write log(x⁴y³/z) in terms of a, b and c.
- A. 4a3b − c
- B. 4a + 3b − c
- C. 4a + 3b + c
- D. 7a − c
11
Question 11
Grace says log(x⁴) = (log x)⁴. Which is the correct rewrite of log(x⁴)?
- A. 4 log x
- B. (log x)⁴
- C. log x ÷ 4
- D. log 4 + log x
12
Question 12
a = log x, b = log y and c = log z. Write log(xy³/z) in terms of a, b and c.
- A. a3b − c
- B. 4a − c
- C. a + 3b − c
- D. a × 3b ÷ c
13
Question 13
Luis says log(x²) = (log x)². Which is the correct rewrite of log(x²)?
- A. (log x)²
- B. log x ÷ 2
- C. 2 log x
- D. log 2 + log x
14
Question 14
a = log x, b = log y and c = log z. Write log(x³y³/z³) in terms of a, b and c.
- A. 3a + 3b − 3c
- B. 3a × 3b ÷ 3c
- C. 3a + 3b + 3c
- D. 6a − 3c
15
Question 15
Diego says log(x³) = (log x)³. Which is the correct rewrite of log(x³)?
- A. log 3 + log x
- B. log x ÷ 3
- C. 3 log x
- D. (log x)³
16
Question 16
a = log x, b = log y and c = log z. Write log(x²y²/z³) in terms of a, b and c.
- A. 2a + 2b − 3c
- B. 2a × 2b ÷ 3c
- C. 4a − 3c
- D. 2a + 2b + 3c

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