Logarithmic heatmap in Plotly

I am using heatmap from Plotly. I want to use a logarithmic scale for the color but cannot find how to do so. Here is a MWE:

import plotly.graph_objects as go
import numpy as np

z = [[1e-4,1e-3,1e-2],
    [1e-1, 1, 1e1],
    [1e2, 1e3, 1e4]]

go.Figure(
    data = go.Heatmap(
        z = z,
    )
).show()

go.Figure(
    data = go.Heatmap(
        z = np.log(z),
    )
).show()

In the MWE I manually calculate the logarithm of the data. I want the color map to be shown as in the second figure but without having to manually transform the data, and also displaying the real z values in the color scale, not the logarithm.

from Logarithmic heatmap in Plotly