Moderate -0.8 This is a straightforward exponential equation requiring a standard technique: take logarithms of both sides, apply log laws, and solve the resulting linear equation. It's simpler than average A-level questions as it's purely procedural with no problem-solving element, though not trivial since students must correctly manipulate logarithms.
Use law for the logarithm of a product, a quotient or a power | M1* |
Obtain $x\log 5 = (2x+1)\log 2$, or equivalent | A1 |
Solve for $x$, via correct manipulative technique(s) | M1(dep*) |
Obtain answer $x = 3.11$. Allow $x \in [3.10, 3.11]$ | A1 | [4]
2 Use logarithms to solve the equation $5 ^ { x } = 2 ^ { 2 x + 1 }$, giving your answer correct to 3 significant figures.
\hfill \mbox{\textit{CAIE P2 2010 Q2 [4]}}