With a horizontal log-scaled color bar and logged labels along the bottom, is it possible to show the exponentiated (original) values along the top?

So in this example, there should be ticks and labels along the top of the color bar going from `mat.min() = 0.058` to `mat.max() = 13.396`

```py
import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np

mat = np.exp(np.random.randn(20, 20))

plt.matshow(mat)

norm = mpl.colors.Normalize(1, np.log(mat.max()))
plt.colorbar(plt.cm.ScalarMappable(norm=norm), orientation="horizontal")

plt.savefig("rand_mat.png", dpi=200)

```

[![random matrix](https://i.stack.imgur.com/ThabF.png)](https://i.stack.imgur.com/ThabF.png)