Standard +0.3 This is a straightforward exponential inequality requiring taking logarithms of both sides and rearranging to isolate x. It's slightly easier than average as it follows a standard procedure with no conceptual tricks, though students must be careful with the direction of the inequality and combining logarithm terms correctly.
Obtain a correct linear inequality in any form, e.g. \(\ln 2 + (1-2x)\ln 3 < x \ln 5\)
A1
Solve for \(x\)
M1
Obtain \(x > \dfrac{\ln 6}{\ln 45}\)
A1
Total
4
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| Use law of the logarithm of a product or power | M1 | |
| Obtain a correct linear inequality in any form, e.g. $\ln 2 + (1-2x)\ln 3 < x \ln 5$ | A1 | |
| Solve for $x$ | M1 | |
| Obtain $x > \dfrac{\ln 6}{\ln 45}$ | A1 | |
| **Total** | **4** | |
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1 Find the set of values of $x$ for which $2 \left( 3 ^ { 1 - 2 x } \right) < 5 ^ { x }$. Give your answer in a simplified exact form. [4]\\
\hfill \mbox{\textit{CAIE P3 2020 Q1 [4]}}