6. (a) Find, to 3 significant figures, the value of x for which 8^x = 0.8 - Edexcel - A-Level Maths Pure - Question 7 - 2007 - Paper 2

We start with the equation:

$$2 ext{log}_1 x - ext{log}_1 (7x) = 1.$$

Using the properties of logarithms, we can rewrite the second term:

$$ext{log}_1 (7x) = ext{log}_1 7 + ext{log}_1 x.$$

Substituting this back into the equation, we have:

$$2 ext{log}_1 x - ( ext{log}_1 7 + ext{log}_1 x) = 1.$$

This simplifies to:

$$ext{log}_1 x = 1 + ext{log}_1 7.$$

Now, we can rearrange and exponentiate:

$$ext{log}_1 x = ext{log}_1 (7 imes 10^1) = ext{log}_1 70.$$

Thus, we find:

$$x = 70.$$