Easy -1.2 This is a straightforward exponential equation requiring only the standard technique of taking logarithms of both sides and applying log laws to solve for x. It's a single-step problem with no conceptual difficulty beyond routine application of logarithm rules, making it easier than average for A-level.
Apply logarithms to both sides and apply power law correctly at least once
\*M1
OE with \(x\) not in a power
Obtain \(x\ln 12 = (2x+1)\ln 3\)
A1
Attempt solution of linear equation
DM1
Obtain \(3.82\)
A1
Do not condone incorrect use of logarithms or greater accuracy
4
**Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Apply logarithms to both sides and apply power law correctly at least once | \*M1 | OE with $x$ not in a power |
| Obtain $x\ln 12 = (2x+1)\ln 3$ | A1 | |
| Attempt solution of linear equation | DM1 | |
| Obtain $3.82$ | A1 | Do not condone incorrect use of logarithms or greater accuracy |
| | **4** | |
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1 Use logarithms to solve the equation $12 ^ { x } = 3 ^ { 2 x + 1 }$. Give your answer correct to 3 significant figures.\\
\hfill \mbox{\textit{CAIE P2 2023 Q1 [4]}}