diff --git a/lib/matplotlib/colors.py b/lib/matplotlib/colors.py
index 865b621d16d1..c6afe628cf19 100644
--- a/lib/matplotlib/colors.py
+++ b/lib/matplotlib/colors.py
@@ -1251,7 +1251,6 @@ def __init__(self, *args, **kwargs):
                 **{k: ba.arguments.pop(k) for k in ["vmin", "vmax", "clip"]})
             self._scale = scale_cls(axis=None, **ba.arguments)
             self._trf = self._scale.get_transform()
-            self._inv_trf = self._trf.inverted()
 
         def __call__(self, value, clip=None):
             value, is_scalar = self.process_value(value)
@@ -1283,7 +1282,10 @@ def inverse(self, value):
                 raise ValueError("Invalid vmin or vmax")
             rescaled = value * (t_vmax - t_vmin)
             rescaled += t_vmin
-            return self._inv_trf.transform(rescaled).reshape(np.shape(value))
+            return (self._trf
+                    .inverted()
+                    .transform(rescaled)
+                    .reshape(np.shape(value)))
 
     Norm.__name__ = base_norm_cls.__name__
     Norm.__qualname__ = base_norm_cls.__qualname__
diff --git a/lib/matplotlib/image.py b/lib/matplotlib/image.py
index 2ef2226dc0bf..17b4da2d16f0 100644
--- a/lib/matplotlib/image.py
+++ b/lib/matplotlib/image.py
@@ -534,9 +534,13 @@ def _make_image(self, A, in_bbox, out_bbox, clip_bbox, magnification=1.0,
                 resampled_masked = np.ma.masked_array(A_resampled, out_mask)
                 # we have re-set the vmin/vmax to account for small errors
                 # that may have moved input values in/out of range
+                s_vmin, s_vmax = vrange
+                if isinstance(self.norm, mcolors.LogNorm):
+                    if s_vmin < 0:
+                        s_vmin = max(s_vmin, np.finfo(scaled_dtype).eps)
                 with cbook._setattr_cm(self.norm,
-                                       vmin=vrange[0],
-                                       vmax=vrange[1],
+                                       vmin=s_vmin,
+                                       vmax=s_vmax,
                                        ):
                     output = self.norm(resampled_masked)
             else:
diff --git a/lib/matplotlib/tests/test_image.py b/lib/matplotlib/tests/test_image.py
index 1b9dd306a4dc..80803d576464 100644
--- a/lib/matplotlib/tests/test_image.py
+++ b/lib/matplotlib/tests/test_image.py
@@ -1204,3 +1204,22 @@ def test_imshow_quantitynd():
     ax.imshow(arr)
     # executing the draw should not raise an exception
     fig.canvas.draw()
+
+
+@check_figures_equal(extensions=['png'])
+def test_huge_range_log(fig_test, fig_ref):
+    data = np.full((5, 5), -1, dtype=np.float64)
+    data[0:2, :] = 1E20
+
+    ax = fig_test.subplots()
+    im = ax.imshow(data, norm=colors.LogNorm(vmin=100, vmax=data.max()),
+                   interpolation='nearest', cmap='viridis')
+
+    data = np.full((5, 5), -1, dtype=np.float64)
+    data[0:2, :] = 1000
+
+    cm = copy(plt.get_cmap('viridis'))
+    cm.set_under('w')
+    ax = fig_ref.subplots()
+    im = ax.imshow(data, norm=colors.Normalize(vmin=100, vmax=data.max()),
+                   interpolation='nearest', cmap=cm)