21N.1.AHL.TZ0.3

attempt to use change the base                (M1)

${\log }_3 \sqrt{x}=\frac{{\log }_3 2}{2}+{\log }_3\left(4x^3\right)$

attempt to use the power rule                (M1)

${\log }_3 \sqrt{x}={\log }_3 \sqrt{2}+{\log }_3\left(4x^3\right)$

attempt to use product or quotient rule for logs, $\ln a+\ln b=\ln ab$                (M1)

${\log }_3 \sqrt{x}={\log }_3 \left(4\sqrt{2}{x}^3\right)$

Note: The M marks are for attempting to use the relevant log rule and may be applied in any order and at any time during the attempt seen.

$\sqrt{x}=4\sqrt{2}{x}^3$

$x=32x^6$

$x^5=\frac{1}{32}$                (A1)

$x=\frac{1}{2}$                A1

 

[5 marks]

[N/A]