To produce linearly and logarithmically spaced arrays in C, a for loop is typically used alongside an initial value and an increment. For linear spacing, an array is filled by incrementing a starting value by a fixed linear step size. For logarithmic spacing, the process involves calculating the step size based on the logarithmic scale. In the example provided, to create 12 logarithmically distributed samples starting from log(2) to 10, the step size is determined using the formula (10 - log(2))/12, although this approach can be confusing. The correct implementation involves initializing the first element of the array with log(2) and calculating the step size using the formula pow(10.0 / array[0], 1./11.) to ensure proper logarithmic spacing. The loop then populates the array by multiplying the previous value by the calculated step size. This method effectively mimics MATLAB's linspace and logspace functions in C.