6. (a) Find, to 3 significant figures, the value of x for which 8^x = 0.8 - Edexcel - A-Level Maths Pure - Question 8 - 2007 - Paper 2

To find the value of x, we start by expressing the equation in logarithmic form:

$$8^x = 0.8$$

Taking the logarithm (base 10) of both sides gives:

$$ext{log}(8^x) = ext{log}(0.8)$$

Using the power rule of logarithms, we can rewrite it as:

$$x imes ext{log}(8) = ext{log}(0.8)$$

Solving for x:

$$x = \frac{ ext{log}(0.8) }{ ext{log}(8) }$$

Calculating the values:

$$x \\approx \frac{-0.09691}{0.90309} \\approx -0.107$$

Thus, the value of x to 3 significant figures is $-0.107$.