Professor Kakule has two tasks for students. For task a), calculate the total expenditure for hiring the vehicles. The number of executive vans is determined by the product of the two values of x that

Here's a step-by-step solution to Professor Kakule's tasks:

a) Calculate the total expenditure for hiring the vehicles.

The number of executive vans is determined by the product of the two values of $x$ that satisfy the logarithmic equation: $\log_x x - \log_x 8 = 2$.

Step 1: Solve the logarithmic equation.
The equation is $\log_x x - \log_x 8 = 2$.
For $\log_x M$ to be defined, the base $x$ must satisfy $x > 0$ and $x \neq 1$. Also, the argument $M$ must be $M > 0$.
The term $\log_x x$ simplifies to 1