diff --git a/lib/matplotlib/scale.py b/lib/matplotlib/scale.py
index d9026a619212..9d1054fd9a86 100644
--- a/lib/matplotlib/scale.py
+++ b/lib/matplotlib/scale.py
@@ -93,7 +93,7 @@ class LogTransformBase(Transform):
     is_separable = True
     has_inverse = True
 
-    def __init__(self, nonpos):
+    def __init__(self, nonpos='clip'):
         Transform.__init__(self)
         self._clip = {"clip": True, "mask": False}[nonpos]
 
@@ -114,6 +114,10 @@ def transform_non_affine(self, a):
             out[a <= 0] = -1000
         return out
 
+    def __str__(self):
+        return "{}({!r})".format(type(self).__name__,
+            "clip" if self._clip else "mask")
+
 
 class InvertedLogTransformBase(Transform):
     input_dims = 1
@@ -124,6 +128,9 @@ class InvertedLogTransformBase(Transform):
     def transform_non_affine(self, a):
         return ma.power(self.base, a)
 
+    def __str__(self):
+        return "{}()".format(type(self).__name__)
+
 
 class Log10Transform(LogTransformBase):
     base = 10.0
@@ -168,7 +175,7 @@ def inverted(self):
 
 
 class LogTransform(LogTransformBase):
-    def __init__(self, base, nonpos):
+    def __init__(self, base, nonpos='clip'):
         LogTransformBase.__init__(self, nonpos)
         self.base = base
 
@@ -448,7 +455,7 @@ class LogitTransform(Transform):
     is_separable = True
     has_inverse = True
 
-    def __init__(self, nonpos):
+    def __init__(self, nonpos='mask'):
         Transform.__init__(self)
         self._nonpos = nonpos
         self._clip = {"clip": True, "mask": False}[nonpos]
@@ -465,6 +472,10 @@ def transform_non_affine(self, a):
     def inverted(self):
         return LogisticTransform(self._nonpos)
 
+    def __str__(self):
+        return "{}({!r})".format(type(self).__name__,
+            "clip" if self._clip else "mask")
+
 
 class LogisticTransform(Transform):
     input_dims = 1
@@ -483,6 +494,9 @@ def transform_non_affine(self, a):
     def inverted(self):
         return LogitTransform(self._nonpos)
 
+    def __str__(self):
+        return "{}({!r})".format(type(self).__name__, self._nonpos)
+
 
 class LogitScale(ScaleBase):
     """
diff --git a/lib/matplotlib/tests/test_scale.py b/lib/matplotlib/tests/test_scale.py
index 9b78377b26bc..c50a0a89609c 100644
--- a/lib/matplotlib/tests/test_scale.py
+++ b/lib/matplotlib/tests/test_scale.py
@@ -1,7 +1,8 @@
-from __future__ import print_function
+from __future__ import print_function, unicode_literals
 
 from matplotlib.testing.decorators import image_comparison
 import matplotlib.pyplot as plt
+from matplotlib.scale import Log10Transform, InvertedLog10Transform
 import numpy as np
 import io
 import pytest
@@ -74,6 +75,27 @@ def test_extra_kwargs_raise():
         ax.set_yscale('log', nonpos='mask')
 
 
+def test_logscale_invert_transform():
+    fig, ax = plt.subplots()
+    ax.set_yscale('log')
+    # get transformation from data to axes
+    tform = (ax.transAxes + ax.transData.inverted()).inverted()
+
+    # direct test of log transform inversion
+    assert isinstance(Log10Transform().inverted(), InvertedLog10Transform)
+
+
+def test_logscale_transform_repr():
+    # check that repr of log transform succeeds
+    fig, ax = plt.subplots()
+    ax.set_yscale('log')
+    s = repr(ax.transData)
+
+    # check that repr of log transform returns correct string
+    s = repr(Log10Transform(nonpos='clip'))
+    assert s == "Log10Transform({!r})".format('clip')
+
+
 @image_comparison(baseline_images=['logscale_nonpos_values'], remove_text=True,
                   extensions=['png'], style='mpl20')
 def test_logscale_nonpos_values():