Moderate -0.8 Part (a) is a straightforward one-step natural logarithm equation requiring only the definition of ln (exponentiating both sides) - a routine C3 skill. Part (b) requires finding a counter-example by testing values where the expression inside ln is less than 1, which is basic but requires slightly more thought than pure recall. Overall, this is easier than average A-level questions due to minimal steps and standard techniques.
3. (a) Solve the equation
$$\ln ( 3 x + 1 ) = 2$$
giving your answer in terms of e.
(b) Prove, by counter-example, that the statement
$$\text { "ln } \left( 3 x ^ { 2 } + 5 x + 3 \right) \geq 0 \text { for all real values of } x \text { " }$$
is false.
3. (a) Solve the equation
$$\ln ( 3 x + 1 ) = 2$$
giving your answer in terms of e.\\
(b) Prove, by counter-example, that the statement
$$\text { "ln } \left( 3 x ^ { 2 } + 5 x + 3 \right) \geq 0 \text { for all real values of } x \text { " }$$
is false.\\
\hfill \mbox{\textit{Edexcel C3 Q3 [8]}}