The natural logarithm ln xEdexcel International A Level Maths: Mind map

Exam questions on The natural logarithm ln x

1. The function $f$ is defined by $f(x)=\ln(3x-2)$, where $x$ takes the largest possible domain.
   Find the exact solution of $f(x)=-2$.2 marks
2. The functions $g$ and $h$ are defined by $g(x)=e^{x}$ and $h(x)=\ln x$, for $x>0$ in the case of $h$.
   State the equation of the asymptote of the graph of $y=h(x)$ and the coordinates of the point where it crosses the $x$-axis.2 marks
3. The curve $C$ has equation $y=\ln(2x+5)$.
   Show that the solution of $\ln(2x+5)=3$ is $x=\frac{e^{3}-5}{2}$ and find its value to 3 significant figures.3 marks