1.5: Estimate roots using a graph

4PM1/1R/June/2025 — Question 7 · 10 marks

(a) Complete the table of values for

y = 3 \mathrm{log}_3(x^2 - x) - 2x

giving your answers to 2 decimal places.

$x$	1.3	1.5	2	2.5	3	3.5
$y$		-3.79	-2.11

(2)

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

y = 3 \mathrm{log}_3(x^2 - x) - 2x

for

1.3 \leq x \leq 3.5

(2)

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

3^{\frac{4}{3}x} = 9(x^2 - x)^3 \quad \text{in the interval } 1.3 \leq x \leq 3.5

(6)