Solve (a) $s^5 = 8$, giving your answer to 3 significant figures, (b) $\log_2 (x + 1) - \log_2 x = \log_2 7.$ - Edexcel - A-Level Maths Pure - Question 5 - 2005 - Paper 2

To solve the equation, we can use the properties of logarithms. Recall that:

$\log_a b - \log_a c = \log_a \frac{b}{c}$

Thus, we can rewrite the left side:

$\log_2 \frac{x + 1}{x} = \log_2 7$

By exponentiating both sides, we eliminate the logarithm:

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

This simplifies to:

$x + 1 = 7x$

Rearranging gives:

$1 = 7x - x \\ 1 = 6x \\ x = \frac{1}{6}$

Thus, the solution for $x$ is:

$x \approx 0.167$