Moderate -0.8 This is a straightforward exponential equation requiring only the standard technique of taking logarithms of both sides and rearranging to solve for x. It's a single-step method with no conceptual difficulty beyond basic log laws, making it easier than average but not trivial since it requires algebraic manipulation after applying logs.
Introduce logarithms to both sides and use power law
\*M1
Obtain \((3x-1)\log 5 = 4x\log 2\) or equivalent
A1
Allow A1 for poor use of brackets if recovered later
Solve linear equation for \(x\)
DM1
dep \*M
Obtain \(0.783\)
A1
Allow 3 sf or better
Total
4
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| Introduce logarithms to both sides and use power law | \*M1 | |
| Obtain $(3x-1)\log 5 = 4x\log 2$ or equivalent | A1 | Allow A1 for poor use of brackets if recovered later |
| Solve linear equation for $x$ | DM1 | dep \*M |
| Obtain $0.783$ | A1 | Allow 3 sf or better |
| **Total** | **4** | |
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