Exercise 01: Given ln(u2) − ln(u4) = 4 and ln(u2) + ln(u4) = -12, find the common ratio q, the first term u0, and the general term un.

Here is the solution to :

Part 1: Find the common ratio $q$, the first term $u_0$, and the general term $u_n$.

Step 1: Solve the system of equations for $\ln(u_2)$ and $\ln(u_4)$.
We are given:

$$\ln(u_2) - \ln(u_4) = 4 \quad (1)$$ $$\ln(u_2) + \ln(u_4) = -12 \quad (2)$$

Add equation (1) and equation (2):

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