Show that the sequence `loga ,log((a^2)/b),log((a^3)/(b^2)),log((a^4)/(b^3)), ` forms an A.P.

Explanation

To show that the sequence \( \log a, \log \left(\frac{a^2}{b}\right), \log \left(\frac{a^3}{b^2}\right), \log \left(\frac{a^4}{b^3}\right) \) forms an arithmetic progression (A.P.), we will follow these steps:

### Step 1: Identify the terms of the sequence
Let:
- \( a_1 = \log a \)
- \( a_2 = \log \left(\frac{a^2}{b}\right) \)
- \( a_3 = \log \left(\frac{a^3}{b^2}\right) \)
- \( a_4 = \log \left(\frac{a^4}{b^3}\right) \)
...