19M.1.AHL.TZ2.H_7

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

use of at least one “log rule” applied correctly for the first equation       M1

$\text{lo}{\text{g}}_{2}6x=\text{lo}{\text{g}}_{2}2+2\text{lo}{\text{g}}_{2}y$

$=\text{lo}{\text{g}}_{2}2+\text{lo}{\text{g}}_2{y}^2$

$=\text{lo}{\text{g}}_2\left(2y^2\right)$

$\Rightarrow 6x=2y^2$       A1

use of at least one “log rule” applied correctly for the second equation       M1

$\text{lo}{\text{g}}_6\left(15y-25\right)=1+\text{lo}{\text{g}}_{6}x$

$=\text{lo}{\text{g}}_{6}6+\text{lo}{\text{g}}_{6}x$

$=\text{lo}{\text{g}}_{6}6x$

$\Rightarrow 15y-25=6x$       A1

attempt to eliminate $x$ (or $y$) from their two equations       M1

$2y^2=15y-25$

$2y^2-15y+25=0$

$\left(2y-5\right)\left(y-5\right)=0$

$x=\frac{25}{12}\text{,}y=\frac{5}{2}\text{,}$       A1

or $x=\frac{25}{3}\text{,}y=5$       A1

Note: $x$, $y$ values do not have to be “paired” to gain either of the final two A marks.

[7 marks]

[N/A]