Hint
Logarithm arguments are positive. Apply the product, quotient or power law to positive arguments.
Worked solution
(a)
Apply the product, quotient or power law to positive arguments.
5
Answer: \(5\)
(b)
Apply the product, quotient or power law to positive arguments.
\(\displaystyle 5+1=6\)
Answer: \(6\)
(c)
Apply the product, quotient or power law to positive arguments.
\(\displaystyle 5-1=4\)
Answer: \(4\)
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: There is no logarithm-of-a-sum addition rule.
(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 omit restrictions when combining logs.
(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: There is no logarithm-of-a-sum addition rule.
Total: 6 marks.