Assertion (A): If log x = $\dfrac{\text{ log } 8}{\text{ log } 0.25}$, then x = -6.

Reason (R): If log _a b = log _a c, then b = c.

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Expand $\text{log}_a \space {\sqrt[3]{x^7y^8 ÷ \sqrt[4]{z}}}$

Prove the following:

$(\text{log} \space x)^2 - (\text{log} \space y)^2 = \text{log} \space \dfrac{x}{y}.\text{log} \space xy$

Prove the following:

$2\text{log} \space \dfrac{11}{13} + \text{log} \space \dfrac{130}{77} - \text{log} \space \dfrac{55}{91} = \text{log} \space 2.$