Hint
Common logarithms have base 10. Apply the product, quotient or power law to positive arguments.
Worked solution
(a)
Apply the product, quotient or power law to positive arguments.
4
Answer: \(4\)
(b)
Apply the product, quotient or power law to positive arguments.
\(\displaystyle 4+4=8\)
Answer: \(8\)
(c)
Apply the product, quotient or power law to positive arguments.
\(\displaystyle 4-4=0\)
Answer: \(0\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternatives and consequential reasoning; an unexplained final answer does not earn a method mark.
(a) · 2 marks
- 1 mark: Apply the product, quotient or power law to positive arguments.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: A reciprocal power has a negative logarithm.
(b) · 2 marks
- 1 mark: Apply the product, quotient or power law to positive arguments.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Do not use a logarithm-of-a-sum rule.
(c) · 2 marks
- 1 mark: Apply the product, quotient or power law to positive arguments.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: A reciprocal power has a negative logarithm.
Total: 6 marks.