Moderate -0.8 This is a straightforward application of logarithms to solve an exponential equation—a standard technique taught early in A-level. It requires taking logs of both sides, using log laws to bring down powers, rearranging to collect x terms, and calculator work. No problem-solving insight needed, just routine procedural execution.
Use law for the logarithm of a power at least once
*M1
Obtain correct linear equation, e.g. \(5\ln2 = (2x + 1)\ln3\)
A1
Solve a linear equation for \(x\)
M1 dep *M
Obtain \(x = 0.866\)
A1
[4]
Use law for the logarithm of a power at least once | *M1 |
Obtain correct linear equation, e.g. $5\ln2 = (2x + 1)\ln3$ | A1 |
Solve a linear equation for $x$ | M1 dep *M |
Obtain $x = 0.866$ | A1 | [4]