diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index b564fb6df1b1..d89d6119c0bb 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -882,6 +882,13 @@ def test_LogFormatter_call(self, val):
         temp_lf.axis = FakeAxis()
         assert temp_lf(val) == str(val)
 
+    @pytest.mark.parametrize('val', [1e-323, 2e-323, 10e-323, 11e-323])
+    def test_LogFormatter_call_tiny(self, val):
+        # test coeff computation in __call__
+        temp_lf = mticker.LogFormatter()
+        temp_lf.axis = FakeAxis()
+        temp_lf(val)
+
 
 class TestLogitFormatter:
     @staticmethod
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index 7a5e3ea60501..21097e282c73 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -1070,7 +1070,7 @@ def __call__(self, x, pos=None):
         fx = math.log(x) / math.log(b)
         is_x_decade = is_close_to_int(fx)
         exponent = round(fx) if is_x_decade else np.floor(fx)
-        coeff = round(x / b ** exponent)
+        coeff = round(b ** (fx - exponent))
 
         if self.labelOnlyBase and not is_x_decade:
             return ''
@@ -1154,7 +1154,7 @@ def __call__(self, x, pos=None):
         fx = math.log(x) / math.log(b)
         is_x_decade = is_close_to_int(fx)
         exponent = round(fx) if is_x_decade else np.floor(fx)
-        coeff = round(x / b ** exponent)
+        coeff = round(b ** (fx - exponent))
         if is_x_decade:
             fx = round(fx)
 
@@ -1186,7 +1186,7 @@ def _non_decade_format(self, sign_string, base, fx, usetex):
         """Return string for non-decade locations."""
         b = float(base)
         exponent = math.floor(fx)
-        coeff = b ** fx / b ** exponent
+        coeff = b ** (fx - exponent)
         if is_close_to_int(coeff):
             coeff = round(coeff)
         return r'$\mathdefault{%s%g\times%s^{%d}}$' \