2. Solve (a) $s^5 = 8$, giving your answer to 3 significant figures, (b) $ ext{log}_2 (x + 1) - ext{log}_2 x = ext{log}_2 7.$ - Edexcel - A-Level Maths Pure - Question 4 - 2005 - Paper 2

Starting with the equation:

$\text{log}_2 (x + 1) - \text{log}_2 x = \text{log}_2 7,$

we can apply the properties of logarithms. This simplifies to:

$\text{log}_2 \left(\frac{x + 1}{x}\right) = \text{log}_2 7.$

Setting the arguments equal gives us:

$\frac{x + 1}{x} = 7,$

which leads to:

$x + 1 = 7x.$

Solving for $x$, we get:

$1 = 6x \Rightarrow x = \frac{1}{6}.$

Thus, the solution is $x = \frac{1}{6}$.