diff --git a/lib/matplotlib/backends/backend_ps.py b/lib/matplotlib/backends/backend_ps.py
index b5263f8fbe66..818b17a39801 100644
--- a/lib/matplotlib/backends/backend_ps.py
+++ b/lib/matplotlib/backends/backend_ps.py
@@ -265,6 +265,21 @@ def __init__(self, width, height, pswriter, imagedpi=72):
         self._path_collection_id = 0
 
         self._character_tracker = _backend_pdf_ps.CharacterTracker()
+        self._logwarn_once = functools.lru_cache(None)(_log.warning)
+
+    def _is_transparent(self, rgb_or_rgba):
+        if rgb_or_rgba is None:
+            return True  # Consistent with rgbFace semantics.
+        elif len(rgb_or_rgba) == 4:
+            if rgb_or_rgba[3] == 0:
+                return True
+            if rgb_or_rgba[3] != 1:
+                self._logwarn_once(
+                    "The PostScript backend does not support transparency; "
+                    "partially transparent artists will be rendered opaque.")
+            return False
+        else:  # len() == 3.
+            return False
 
     def set_color(self, r, g, b, store=True):
         if (r, g, b) != self.color:
@@ -457,7 +472,7 @@ def draw_markers(
 
         ps_color = (
             None
-            if _is_transparent(rgbFace)
+            if self._is_transparent(rgbFace)
             else '%1.3f setgray' % rgbFace[0]
             if rgbFace[0] == rgbFace[1] == rgbFace[2]
             else '%1.3f %1.3f %1.3f setrgbcolor' % rgbFace[:3])
@@ -552,7 +567,7 @@ def draw_path_collection(self, gc, master_transform, paths, all_transforms,
     def draw_tex(self, gc, x, y, s, prop, angle, *, mtext=None):
         # docstring inherited
         if not hasattr(self, "psfrag"):
-            _log.warning(
+            self._logwarn_once(
                 "The PS backend determines usetex status solely based on "
                 "rcParams['text.usetex'] and does not support having "
                 "usetex=True only for some elements; this element will thus "
@@ -589,7 +604,7 @@ def draw_tex(self, gc, x, y, s, prop, angle, *, mtext=None):
     def draw_text(self, gc, x, y, s, prop, angle, ismath=False, mtext=None):
         # docstring inherited
 
-        if _is_transparent(gc.get_rgb()):
+        if self._is_transparent(gc.get_rgb()):
             return  # Special handling for fully transparent.
 
         if ismath == 'TeX':
@@ -729,10 +744,10 @@ def _draw_ps(self, ps, gc, rgbFace, *, fill=True, stroke=True):
         """
         write = self._pswriter.write
         mightstroke = (gc.get_linewidth() > 0
-                       and not _is_transparent(gc.get_rgb()))
+                       and not self._is_transparent(gc.get_rgb()))
         if not mightstroke:
             stroke = False
-        if _is_transparent(rgbFace):
+        if self._is_transparent(rgbFace):
             fill = False
         hatch = gc.get_hatch()
 
@@ -769,21 +784,6 @@ def _draw_ps(self, ps, gc, rgbFace, *, fill=True, stroke=True):
         write("grestore\n")
 
 
-def _is_transparent(rgb_or_rgba):
-    if rgb_or_rgba is None:
-        return True  # Consistent with rgbFace semantics.
-    elif len(rgb_or_rgba) == 4:
-        if rgb_or_rgba[3] == 0:
-            return True
-        if rgb_or_rgba[3] != 1:
-            _log.warning(
-                "The PostScript backend does not support transparency; "
-                "partially transparent artists will be rendered opaque.")
-        return False
-    else:  # len() == 3.
-        return False
-
-
 @_api.deprecated("3.4", alternative="GraphicsContextBase")
 class GraphicsContextPS(GraphicsContextBase):
     def get_capstyle(self):
diff --git a/lib/matplotlib/tests/test_backend_ps.py b/lib/matplotlib/tests/test_backend_ps.py
index 57215367ab3b..a70145cc6d2d 100644
--- a/lib/matplotlib/tests/test_backend_ps.py
+++ b/lib/matplotlib/tests/test_backend_ps.py
@@ -149,10 +149,11 @@ def test_failing_latex():
 @needs_usetex
 def test_partial_usetex(caplog):
     caplog.set_level("WARNING")
-    plt.figtext(.5, .5, "foo", usetex=True)
+    plt.figtext(.1, .1, "foo", usetex=True)
+    plt.figtext(.2, .2, "bar", usetex=True)
     plt.savefig(io.BytesIO(), format="ps")
-    assert caplog.records and all("as if usetex=False" in record.getMessage()
-                                  for record in caplog.records)
+    record, = caplog.records  # asserts there's a single record.
+    assert "as if usetex=False" in record.getMessage()
 
 
 @image_comparison(["useafm.eps"])