from matplotlib import pyplot as plt

# returns a number n' so that base^n = goal and |n - n'| <= epsilon
def log(base, goal, epsilon = 1e-8):
    assert base > 0 and base != 1 and goal > 0, 'bad argument for log function: base={}, goal={}'.format(base, goal)

    if goal == 1:
        return 0

    if base > 1e1 or base < 1e-1:
        return 0.5*log(base**0.5, goal)

    if goal > 1e2 or goal < 1e-2:
        return 2*log(base, goal**0.5)

    ma = 2*max(base, goal, base/goal, goal/base)
    mi = -ma
    while ma-mi > epsilon:
        #print(mi, ma)
        av = (ma+mi)/2
        if base > 1:
            if base**av < goal:
                mi = (ma+mi)/2
            else:
                ma = (ma+mi)/2
        else:
            if base**av < goal:
                ma = (ma+mi)/2
            else:
                mi = (ma+mi)/2
    
    return mi

xs = []
step = 0.025
max_x = 8
x = step
while x < max_x:
    xs.append(x)
    x += step
ys = [log(3000000, x) for x in xs]
plt.plot(xs, ys)
plt.show()