Moderate -0.8 This is a straightforward logarithm manipulation question requiring students to take logs of both sides and rearrange to isolate y. It's a standard textbook exercise testing basic log laws with no problem-solving insight needed, making it easier than average but not trivial since it requires correct algebraic manipulation.
1 Given that \(5 ^ { x } = 3 ^ { 4 y }\), use logarithms to show that \(y = m x\) and find the value of the constant \(m\) correct to 3 significant figures.
Take logarithms of both sides and apply power law to both sides
M1
Allow \(y = \frac{\log 5}{4\log 3}\) for M1 A1
Rearrange to the form \(y = \frac{\ln 5}{4\ln 3}x\) or equivalent
A1
Obtain \(m = 0.366\)
A1
Total:
3
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Take logarithms of both sides and apply power law to both sides | M1 | Allow $y = \frac{\log 5}{4\log 3}$ for M1 A1 |
| Rearrange to the form $y = \frac{\ln 5}{4\ln 3}x$ or equivalent | A1 | |
| Obtain $m = 0.366$ | A1 | |
| **Total:** | **3** | |
1 Given that $5 ^ { x } = 3 ^ { 4 y }$, use logarithms to show that $y = m x$ and find the value of the constant $m$ correct to 3 significant figures.\\
\hfill \mbox{\textit{CAIE P2 2017 Q1 [3]}}