Moderate -0.8 This is a straightforward exponential equation requiring a standard technique (taking logarithms of both sides, applying log laws, and rearranging to isolate x). It's a single-step problem with no conceptual difficulty beyond knowing the basic method, making it easier than average but not trivial since it requires proper application of logarithm properties.
Use law for the logarithm of a product, a quotient or a power
M1*
Obtain \(x\ln 4 = \ln 2 + x\ln 3\), or equivalent
A1
Solve for \(x\)
M1 (dep*)
Obtain answer \(x = 2.41\)
A1
[4]
Use law for the logarithm of a product, a quotient or a power | M1* |
Obtain $x\ln 4 = \ln 2 + x\ln 3$, or equivalent | A1 |
Solve for $x$ | M1 (dep*) |
Obtain answer $x = 2.41$ | A1 |
| [4] |
2 Use logarithms to solve the equation $4 ^ { x } = 2 \left( 3 ^ { x } \right)$, giving your answer correct to 3 significant figures.
\hfill \mbox{\textit{CAIE P2 2008 Q2 [4]}}