Moderate -0.8 This is a straightforward application of logarithms to solve an exponential equation. It requires taking ln of both sides, using log laws to bring down the powers, rearranging to collect x terms, and factoring—all standard techniques with no conceptual difficulty or multi-step problem-solving required.
Obtain a correct linear equation in any form, e.g. \(x = (x - 2) \ln 3\)
A1
Obtain answer \(x = -22.281\)
A1
[3]
Use law of the logarithm of a power | M1 |
Obtain a correct linear equation in any form, e.g. $x = (x - 2) \ln 3$ | A1 |
Obtain answer $x = -22.281$ | A1 | [3]
1 Use logarithms to solve the equation $\mathrm { e } ^ { x } = 3 ^ { x - 2 }$, giving your answer correct to 3 decimal places.
\hfill \mbox{\textit{CAIE P3 2014 Q1 [3]}}