Moderate -0.8 This is a straightforward exponential equation requiring only the standard technique of taking logarithms of both sides and rearranging. It's a routine textbook exercise with a single clear method and no conceptual challenges, making it easier than average but not trivial since students must correctly manipulate logarithms and solve for x.
Use law for the logarithm of a product, a quotient or a power | M1* |
Obtain $x \log 5 = (2x - 1) \log 3$ or equivalent | A1 |
Solve for $x$ | M1(dep*) |
Obtain answer $x = 1.87$ | A1 | [4]
2 Use logarithms to solve the equation $5 ^ { x } = 3 ^ { 2 x - 1 }$, giving your answer correct to 3 significant figures.
\hfill \mbox{\textit{CAIE P2 2012 Q2 [4]}}