Moderate -0.8 This is a straightforward logarithm manipulation requiring only taking logs of both sides, applying log laws, and rearranging to isolate y. It's a standard textbook exercise with a clear method and no problem-solving insight needed, making it easier than average.
1 Use logarithms to show that the equation \(5 ^ { 8 y } = 6 ^ { 7 x }\) can be expressed in the form \(y = k x\). Give the value of the constant \(k\) correct to 3 significant figures.
May be implied by 0.97, 0.973 seen. May use a different base.
Obtain \(k = 0.974\) or state \(y = 0.974x\)
A1
Or greater accuracy.
Total
3
**Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Apply logarithms correctly and apply power law at least once | \*M1 | |
| Obtain $y = \dfrac{7\ln 6}{8\ln 5}\, x$ or equivalent perhaps involving decimals | DM1 | May be implied by 0.97, 0.973 seen. May use a different base. |
| Obtain $k = 0.974$ or state $y = 0.974x$ | A1 | Or greater accuracy. |
| **Total** | **3** | |
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1 Use logarithms to show that the equation $5 ^ { 8 y } = 6 ^ { 7 x }$ can be expressed in the form $y = k x$. Give the value of the constant $k$ correct to 3 significant figures.\\
\hfill \mbox{\textit{CAIE P2 2024 Q1 [3]}}