Moderate -0.3 This is a straightforward numerical methods question requiring rearrangement to f(x)=0 form, then applying interval bisection or iteration. The algebraic manipulation is simple (ln(1+x) - ln(x) = 1), and the numerical method is standard bookwork. Slightly easier than average as it's a direct application with no conceptual challenges, though it does require proper execution of the numerical technique.
Use law for subtraction or addition of logarithms, or the equivalent in exponentials
M1
Use \(\ln e = 1\) or \(e = \exp(1)\)
M1
Obtain a correct equation free of logarithms e.g. \(\frac{1+x}{x} = e\) or \(1 + x = ex\)
A1
Obtain answer \(x = 0.58\) (allow 0.582 or answer rounding to it)
A1
Total: 4 marks
Use law for subtraction or addition of logarithms, or the equivalent in exponentials | M1 | |
Use $\ln e = 1$ or $e = \exp(1)$ | M1 | |
Obtain a correct equation free of logarithms e.g. $\frac{1+x}{x} = e$ or $1 + x = ex$ | A1 | |
Obtain answer $x = 0.58$ (allow 0.582 or answer rounding to it) | A1 | **Total: 4 marks** |