Moderate -0.3 This is a straightforward logarithm equation requiring standard log laws (sum and multiple rules), leading to a quadratic equation. The 'fully justify' requirement adds minimal difficulty as students just need to check their solution is in the domain (x > 1). Slightly easier than average due to being a routine application of well-practiced techniques with no conceptual surprises.
Question 4:
4 | Obtains ln(x + 1)(x – 1)
Or
ln(x2 – 1)
PI by correct equation in x2
Condone missing brackets | 1.1b | B1 | ln(x + 1)(x – 1)
= ln15 – ln49
15
= ln
49
15
x2 – 1 =
49
64
x2 =
49
8
x =
7
8
x cannot be – because the ln
7
functions would not exist with this
value
Obtains ln 49 or ln72 for 2 ln 7
PI by correct equation in x2 | 1.1b | B1
Applies subtraction rule for ln to
right-hand side
PI by correct equation in x2 | 1.1a | M1
Obtains correct exact value for
x2
PI | 1.1b | A1
8
Explains why x = - is not a
7
valid solution.
Must refer to ln(-ve) | 2.4 | E1
Question 4 Total | 5
Q | Marking instructions | AO | Marks | Typical solution