1.9: Estimate roots using a graph

4PM1/2/November/2024 — Question 4 · 8 marks

(a) Complete the table of values for

y = \mathrm{log}_{10}(6x-1) - x

giving your answers to 2 decimal places.

$x$	0.25	0.5	1	1.5	2	2.5	3
$y$		-0.20	-0.30	-0.60

(2)

(b) On the grid opposite, draw the graph of

y = \mathrm{log}_{10}(6x-1) - x

for

0.25 \leq x \leq 3

(2)

(c) By drawing a suitable straight line on the grid, obtain an estimate, to one decimal place, of the root of the equation

10^{\frac{3x-4}{2}} = 6x-1 \text{ in the interval } 0.25 \leq x \leq 3

(4)

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