Write `3+2lg a-4lg b` as a single logarithm to base 10.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [B1] for 3=lg1000
2. [B1] for use of power rule once
3. [B1] for use of addition or subtraction rule once
4. [B1] All correct
5. [B1] Either 3log₄4 = 3/log₄a
6. [M1] For obtaining a quadratic equation and solution
7. [M1 Dep] For dealing with the logarithm correctly once, may be implied by a correct solution
8. [A1] 64
9. [A1] 2
10. [(B1)] Or 2log₄a = 2/logₐ4
11. [(M1)] For obtaining a quadratic equation and solution
12. [(M1) Dep] For dealing with the logarithm correctly once, may be implied by a correct solution
13. [(A1)] 64
14. [(A1)] 2