1.43: Estimate roots using a graph

(a) Complete the table of values for $y=\ln(5x+1)+2$ giving your answers to 2 decimal places.

(2)
(b) On the grid opposite draw the graph of $y=\ln(5x+1)+2$ for $0\le x\le7$. (2)

(c) By drawing an appropriate straight line on the grid, obtain an estimate, to 1 decimal place, of the positive root of the equation $\ln(5x+1)-x=0$ in the interval $0\le x\le7$. (3)

(d) By drawing an appropriate straight line on the grid, obtain an estimate, to 1 decimal place, of the root of the equation $e^{(3x-1)}=5x+1$ in the interval $0\le x\le7$. (4)