diff --git a/lib/matplotlib/axes/_secondary_axes.py b/lib/matplotlib/axes/_secondary_axes.py
index 4740fe6b23fb..b9ae2d57d6a3 100644
--- a/lib/matplotlib/axes/_secondary_axes.py
+++ b/lib/matplotlib/axes/_secondary_axes.py
@@ -82,6 +82,7 @@ def __init__(self, parent, orientation,
             self._axis = self.yaxis
             self._locstrings = ['right', 'left']
             self._otherstrings = ['top', 'bottom']
+        self._parentscale = self._axis.get_scale()
         # this gets positioned w/o constrained_layout so exclude:
         self._layoutbox = None
         self._poslayoutbox = None
@@ -272,6 +273,11 @@ def _set_scale(self):
         if self._orientation == 'y':
             pscale = self._parent.yaxis.get_scale()
             set_scale = self.set_yscale
+        if pscale == self._parentscale:
+            return
+        else:
+            self._parentscale = pscale
+
         if pscale == 'log':
             defscale = 'functionlog'
         else:
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 9e1a8c8123d8..9c3570c2bc16 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -24,6 +24,7 @@
 import matplotlib.markers as mmarkers
 import matplotlib.patches as mpatches
 import matplotlib.colors as mcolors
+import matplotlib.ticker as mticker
 import matplotlib.transforms as mtransforms
 from numpy.testing import (
     assert_allclose, assert_array_equal, assert_array_almost_equal)
@@ -6079,6 +6080,29 @@ def invert(x):
     assert_allclose(ax.get_position().extents, [0.125, 0.1, 0.9, 0.9])
 
 
+def test_secondary_minorloc():
+    fig, ax = plt.subplots(figsize=(10, 5))
+    ax.plot(np.arange(2, 11), np.arange(2, 11))
+    def invert(x):
+        with np.errstate(divide='ignore'):
+            return 1 / x
+
+    secax = ax.secondary_xaxis('top', functions=(invert, invert))
+    assert isinstance(secax._axis.get_minor_locator(),
+                      mticker.NullLocator)
+    secax.minorticks_on()
+    assert isinstance(secax._axis.get_minor_locator(),
+                      mticker.AutoMinorLocator)
+    ax.set_xscale('log')
+    plt.draw()
+    assert isinstance(secax._axis.get_minor_locator(),
+                      mticker.LogLocator)
+    ax.set_xscale('linear')
+    plt.draw()
+    assert isinstance(secax._axis.get_minor_locator(),
+                      mticker.NullLocator)
+
+
 def color_boxes(fig, axs):
     """
     Helper for the tests below that test the extents of various axes elements