Moderate -0.8 This is a straightforward logarithm manipulation question requiring only standard log laws (power rule, subtraction rule) and basic algebraic rearrangement. The steps are routine: apply log laws to get 3log_a(x) = log_a(72/9) = log_a(8), then x³ = 8, so x = 2. No problem-solving insight needed, just mechanical application of rules, making it easier than average.
Question 3:
3 | Uses power law for logarithms
at least once | 1.1a | M1 | loga x3 = loga 72 – loga 32
7 2
loga x3 = loga = loga 8
9
x3 = 8
x = 2
Uses subtraction law for
logarithms OE
PI by loga 8 OE
lo g 7 2
Condone a if recovered to
lo g 9
a
loga 8
Condone omission of the base a | 1.1a | M1
Obtains loga 8 on right-hand
side of equation OE
Or
loga 9x3 on left-hand side
Condone omission of the base a | 1.1b | A1
Obtains x = 2 CAO | 1.1b | A1
Question 3 Total | 4
Q | Marking instructions | AO | Marks | Typical solution
It is given that
$$3 \log_a x = \log_a 72 - 2 \log_a 3$$
Solve the equation to find the value of $x$
Fully justify your answer.
[4 marks]
\hfill \mbox{\textit{AQA AS Paper 2 2024 Q3 [4]}}