diff --git a/lib/matplotlib/image.py b/lib/matplotlib/image.py
index 0ab02c403d0d..ce08e2470d2f 100644
--- a/lib/matplotlib/image.py
+++ b/lib/matplotlib/image.py
@@ -452,6 +452,8 @@ def _make_image(self, A, in_bbox, out_bbox, clip_bbox, magnification=1.0,
 
                 # Always copy, and don't allow array subtypes.
                 A_scaled = np.array(A, dtype=scaled_dtype)
+                a_min = np.float64(a_min)
+                a_max = np.float64(a_max)
                 # Clip scaled data around norm if necessary.  This is necessary
                 # for big numbers at the edge of float64's ability to represent
                 # changes.  Applying a norm first would be good, but ruins the
diff --git a/lib/matplotlib/tests/test_colorbar.py b/lib/matplotlib/tests/test_colorbar.py
index 74742d8c2369..cd7f6c223dd3 100644
--- a/lib/matplotlib/tests/test_colorbar.py
+++ b/lib/matplotlib/tests/test_colorbar.py
@@ -1238,3 +1238,48 @@ def test_colorbar_format_string_and_old():
     plt.imshow([[0, 1]])
     cb = plt.colorbar(format="{x}%")
     assert isinstance(cb._formatter, StrMethodFormatter)
+
+
+def test_colorbar_log_units():
+    class FakeQuantity(np.ndarray):
+        # this is a self-contained version of astropy.units.Quantity
+        # reduced to a bare minimum to reproduce
+        # https://github.com/astropy/astropy/issues/11306
+
+        def __new__(cls, value):
+            return np.array(value).view(cls)
+
+        def __array_ufunc__(self, function, method, *inputs, **kwargs):
+            def to_value(q):
+                value = q.view(np.ndarray)
+                if value.shape:
+                    return value
+                else:
+                    return value[()]
+
+            arrays = [to_value(q) for q in inputs]
+            result = super().__array_ufunc__(function, method, *arrays, **kwargs)
+            if function not in (np.minimum, np.maximum):
+                return result
+            else:
+                return self._new_view(result)
+
+        def _new_view(self, obj):
+            obj = np.array(obj, copy=False, subok=True)
+            view = obj.view(FakeQuantity)
+            return view
+
+        def __ne__(self, other):
+            return NotImplemented
+
+        def __float__(self):
+            raise RuntimeError("boom")
+
+        def item(self, *args):
+            return self._new_view(super().item(*args))
+
+    data = FakeQuantity([[1, 2], [3, 4]])
+    fig, ax = plt.subplots()
+    im = ax.imshow(data, norm=LogNorm())
+    fig.colorbar(im)
+    fig.canvas.draw()
diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 5003e2113930..4b0cd1cd035b 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -2853,15 +2853,15 @@ def nonsingular(vmin, vmax, expander=0.001, tiny=1e-15, increasing=True):
     if (not np.isfinite(vmin)) or (not np.isfinite(vmax)):
         return -expander, expander
 
+    # Expand vmin, vmax to float: if they were integer types, they can wrap
+    # around in abs (abs(np.int8(-128)) == -128) and vmax - vmin can overflow.
+    vmin, vmax = map(np.float64, (vmin, vmax))
+
     swapped = False
     if vmax < vmin:
         vmin, vmax = vmax, vmin
         swapped = True
 
-    # Expand vmin, vmax to float: if they were integer types, they can wrap
-    # around in abs (abs(np.int8(-128)) == -128) and vmax - vmin can overflow.
-    vmin, vmax = map(float, [vmin, vmax])
-
     maxabsvalue = max(abs(vmin), abs(vmax))
     if maxabsvalue < (1e6 / tiny) * np.finfo(float).tiny:
         vmin = -expander