Standard +0.3 This is a straightforward logarithmic equation requiring students to take logarithms of both sides, apply log laws to bring down the exponents, collect terms in x, and solve. It's a standard textbook exercise with clear methodology and no conceptual surprises, making it slightly easier than average.
Apply logarithms correctly to both sides and apply power law at least once
\*M1
Obtain \(\ln 14 - 2x = (x+1)\ln 5\)
A1
OE with \(x\) no longer part of a power
Attempt solution of linear equation
DM1
Must have \(\ln 14 - \ln 5 = x(2 + \ln 5)\)
Obtain \(0.285\)
A1
## Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| Apply logarithms correctly to both sides and apply power law at least once | \*M1 | |
| Obtain $\ln 14 - 2x = (x+1)\ln 5$ | A1 | OE with $x$ no longer part of a power |
| Attempt solution of linear equation | DM1 | Must have $\ln 14 - \ln 5 = x(2 + \ln 5)$ |
| Obtain $0.285$ | A1 | |
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