Moderate -0.8 This is a straightforward logarithm application requiring students to take logs of both sides and use basic log laws (log of a power). It's a standard textbook exercise with a clear method and minimal steps, making it easier than average but not trivial since it requires correct manipulation of logarithmic properties.
Apply logarithms to both sides and apply power law at least once
M1
Rearrange to the form \(y = \dfrac{3\ln 9}{\ln 2}x\)
A1
OE
Obtain \(k = 9.51\)
A1
Total
3
**Question 1:**
| Answer | Mark | Guidance |
|--------|------|----------|
| Apply logarithms to both sides and apply power law at least once | M1 | |
| Rearrange to the form $y = \dfrac{3\ln 9}{\ln 2}x$ | A1 | OE |
| Obtain $k = 9.51$ | A1 | |
| **Total** | **3** | |
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1 Given that $2 ^ { y } = 9 ^ { 3 x }$, use logarithms to show that $y = k x$ and find the value of $k$ correct to 3 significant figures.\\
\hfill \mbox{\textit{CAIE P2 2020 Q1 [3]}}