Moderate -0.8 This is a straightforward algebraic manipulation of an exponential equation requiring only cross-multiplication, collecting terms, and taking a logarithm. It's a routine single-step problem with no conceptual difficulty beyond basic exponential laws, making it easier than the average A-level question which typically requires multiple techniques or some problem-solving insight.
Use correct method for solving an equation of the form \(2^x = a\), where \(a > 0\)
M1
Obtain answer \(x = 0.585\)
A1
State an appropriate iterative formula, e.g. \(x_{n+1} = \ln(2^x + 6)/5 / \ln 2\)
B1
Use the iterative formula correctly at least once
M1
Obtain answer \(x = 0.585\)
A1
Show that the equation has no other root but \(0.585\)
A1
[4]
[For the solution 0.585 with no relevant working, award B1 and a further B1 if 0.585 is shown to be the only root.]
Attempt to solve for $2^x$ | M1 |
Obtain $2^x = 6/4$, or equivalent | A1 |
Use correct method for solving an equation of the form $2^x = a$, where $a > 0$ | M1 |
Obtain answer $x = 0.585$ | A1 |
State an appropriate iterative formula, e.g. $x_{n+1} = \ln(2^x + 6)/5 / \ln 2$ | B1 |
Use the iterative formula correctly at least once | M1 |
Obtain answer $x = 0.585$ | A1 |
Show that the equation has no other root but $0.585$ | A1 | [4]
[For the solution 0.585 with no relevant working, award B1 and a further B1 if 0.585 is shown to be the only root.]