Let's go through each question from the image you've provided:

1. Determine the highest common factors of (The question seems to be incomplete in the image, but this typically involves finding the HCF of a set of numbers or algebraic terms.)

2. Solve the following logarithmic equations:

   (i) $\log_5(2x + 4) = 2$

   Solution: Rewrite the equation in exponential form: $2x + 4 = 5^2$ $2x + 4 = 25$ $2x = 21$ $x = \frac{21}{2} = 10.5$

   (ii) $\log_2(x^2 - 6x) = 3 + \log_2(1 - x)$

   Solution: First, use the logarithmic property $\log_a b - \log_a c = \log_a \frac{b}{c}$: $\log_2(x^2 - 6x) - \log_2(1 - x) = 3$ $\log_2\left(\frac{x^2 - 6x}{1 - x}\right) = 3$ Now rewrite this in exponential form: $\frac{x^2 - 6x}{1 - x} = 2^3$ $\frac{x^2 - 6x}{1 - x} = 8$ Multiply both sides by $1 - x$: $x^2 - 6x = 8(1 - x)$ $x^2 - 6x = 8 - 8x$ $x^2 + 2x - 8 = 0$ Solve this quadratic equation using the formula: $x = \frac{-2 \pm \sqrt{(2)^2 + 4 \cdot 8}}{2}$

3. Solve the following quadratic equation:

   [ 3x^