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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Score/ 16
Question 1
a = log x, b = log y and c = log z. Write log(xy²/z²) in terms of a, b and c.
- A. a + 2b − 2c
- B. a × 2b ÷ 2c
- C. 3a − 2c
- D. a + 2b + 2c
Question 2
Yuki says log(x²) = (log x)². Which is the correct rewrite of log(x²)?
- A. log 2 + log x
- B. log x ÷ 2
- C. 2 log x
- D. (log x)²
Question 3
a = log x, b = log y and c = log z. Write log(x³y³/z²) in terms of a, b and c.
- A. 6a − 2c
- B. 3a3b − 2c
- C. 3a × 3b ÷ 2c
- D. 3a + 3b − 2c
Question 4
Ethan says log(x²) = (log x)². Which is the correct rewrite of log(x²)?
- A. 2 log x
- B. (log x)²
- C. log 2 + log x
- D. log x ÷ 2
Question 5
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. 4a − c
- C. 3ab − c
- D. 3a × b ÷ c
Question 6
Kai says log(x²) = (log x)². Which is the correct rewrite of log(x²)?
- A. (log x)²
- B. log x ÷ 2
- C. log 2 + log x
- D. 2 log x
Question 7
a = log x, b = log y and c = log z. Write log(x²y³/z²) in terms of a, b and c.
- A. 2a × 3b ÷ 2c
- B. 2a3b − 2c
- C. 2a + 3b − 2c
- D. 2a + 3b + 2c
Question 8
Ben says log(x⁵) = (log x)⁵. Which is the correct rewrite of log(x⁵)?
- A. log 5 + log x
- B. log x ÷ 5
- C. (log x)⁵
- D. 5 log x
Question 9
a = log x, b = log y and c = log z. Write log(xy/z) in terms of a, b and c.
- A. a × b ÷ c
- B. 2a − c
- C. a + b − c
- D. a + b + c
Question 10
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. log x ÷ 3
- D. 3 log x
Question 11
a = log x, b = log y and c = log z. Write log(x³y²/z²) in terms of a, b and c.
- A. 5a − 2c
- B. 3a2b − 2c
- C. 3a + 2b − 2c
- D. 3a + 2b + 2c
Question 12
Grace says log(x⁴) = (log x)⁴. Which is the correct rewrite of log(x⁴)?
- A. log 4 + log x
- B. log x ÷ 4
- C. (log x)⁴
- D. 4 log x
Question 13
a = log x, b = log y and c = log z. Write log(x³y³/z) in terms of a, b and c.
- A. 3a3b − c
- B. 3a + 3b + c
- C. 3a × 3b ÷ c
- D. 3a + 3b − c
Question 14
Zara says log(x²) = (log x)². Which is the correct rewrite of log(x²)?
- A. 2 log x
- B. (log x)²
- C. log 2 + log x
- D. log x ÷ 2
Question 15
a = log x, b = log y and c = log z. Write log(xy²/z) in terms of a, b and c.
- A. a + 2b + c
- B. 3a − c
- C. a + 2b − c
- D. a2b − c
Question 16
Kai says log(x⁴) = (log x)⁴. Which is the correct rewrite of log(x⁴)?
- A. log x ÷ 4
- B. 4 log x
- C. (log x)⁴
- D. log 4 + log x
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