1.1: Estimate roots using a graph

(a) Complete the table of values for $y = 3^x - 2$ giving your answers to one decimal place.

(b) On the grid opposite, draw the graph of $y = 3^x - 2$ for $-1 \leq x \leq 2$

(c) Use your graph to obtain an estimate, to one decimal place, of the value of $\mathrm{log}_3 4.5$

Show clearly how you have used your graph.

(d) By drawing a straight line on your grid obtain an estimate, to one decimal place, of the root of the equation $\mathrm{log}_3(8-3x) - x = 0$ in the interval $-1 \leq x \leq 2$

Only use this grid if you need to redraw your graph.