1.3: Linear law: lg⁡y\lg y against x2x^{2}

0606/11/M/J/19 — Question 10 · 9 marks

When lg⁡y\lg y is plotted against x2x^{2} a straight line graph is obtained which passes through the points (2,4)(2, 4) and (6,16)(6, 16).
(i)
Show that y=10A+Bx2y = 10^{A + Bx^{2}}, where AA and BB are constants.
[4]
(ii)
Find yy when x=13x = \dfrac{1}{\sqrt{3}}.
[2]
(iii)
Find the positive value of xx when y=2y = 2.
[3]