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

Using the properties of logarithms, we can combine the left side:

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

This implies:

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

Multiplying both sides by $x$ results in:

$x + 1 = 7x$

Rearranging gives:

$1 = 6x$

Finally, we solve for $x$:

$x = \frac{1}{6} \\ \text{(which is approximately 0.167)}$