diff --git a/doc/api/next_api_changes/2019-06-19-AL.rst b/doc/api/next_api_changes/2019-06-19-AL.rst
@@ -0,0 +1,10 @@
+log-scale bar() / hist() autolimits change
+``````````````````````````````````````````
+
+The autolimits computation in `~.Axes.bar` and `~.Axes.hist` when the axes
+already uses log-scale has changed to match the computation when the axes is
+switched to log-scale after the call to `~.Axes.bar` and `~.Axes.hist`, and
+when calling ``bar(..., log=True)`` / ``hist(..., log=True)``: if there are
+at least two different bar heights, add the normal axes margins to them (in
+log-scale); if there is only a single bar height, expand the axes limits by one
+order of magnitude around it and then apply axes margins.
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
@@ -2303,20 +2303,12 @@ def bar(self, x, height, width=0.8, bottom=None, *, align="center",
         label = kwargs.pop('label', '')
         tick_labels = kwargs.pop('tick_label', None)
 
-        adjust_ylim = False
-        adjust_xlim = False
-
         y = bottom  # Matches barh call signature.
         if orientation == 'vertical':
-            if bottom is None:
-                if self.get_yscale() == 'log':
-                    adjust_ylim = True
+            if y is None:
                 y = 0
-
         elif orientation == 'horizontal':
             if x is None:
-                if self.get_xscale() == 'log':
-                    adjust_xlim = True
                 x = 0
 
         if orientation == 'vertical':
@@ -2429,21 +2421,6 @@ def bar(self, x, height, width=0.8, bottom=None, *, align="center",
         else:
             errorbar = None
 
-        if adjust_xlim:
-            xmin, xmax = self.dataLim.intervalx
-            xmin = min(w for w in width if w > 0)
-            if xerr is not None:
-                xmin = xmin - np.max(xerr)
-            xmin = max(xmin * 0.9, 1e-100)
-            self.dataLim.intervalx = (xmin, xmax)
-
-        if adjust_ylim:
-            ymin, ymax = self.dataLim.intervaly
-            ymin = min(h for h in height if h > 0)
-            if yerr is not None:
-                ymin = ymin - np.max(yerr)
-            ymin = max(ymin * 0.9, 1e-100)
-            self.dataLim.intervaly = (ymin, ymax)
         self._request_autoscale_view()
 
         bar_container = BarContainer(patches, errorbar, label=label)
@@ -6741,30 +6718,8 @@ def hist(self, x, bins=None, range=None, density=False, weights=None,
             if log:
                 if orientation == 'horizontal':
                     self.set_xscale('log', nonposx='clip')
-                    logbase = self.xaxis._scale.base
                 else:  # orientation == 'vertical'
                     self.set_yscale('log', nonposy='clip')
-                    logbase = self.yaxis._scale.base
-
-                # Setting a minimum of 0 results in problems for log plots
-                if np.min(bottom) > 0:
-                    minimum = np.min(bottom)
-                elif density or weights is not None:
-                    # For data that is normed to form a probability density,
-                    # set to minimum data value / logbase
-                    # (gives 1 full tick-label unit for the lowest filled bin)
-                    ndata = np.array(tops)
-                    minimum = (np.min(ndata[ndata > 0])) / logbase
-                else:
-                    # For non-normed (density = False) data,
-                    # set the min to 1 / log base,
-                    # again so that there is 1 full tick-label unit
-                    # for the lowest bin
-                    minimum = 1.0 / logbase
-
-                y[0], y[-1] = minimum, minimum
-            else:
-                minimum = 0
 
             if align == 'left':
                 x -= 0.5*(bins[1]-bins[0])
@@ -6785,8 +6740,6 @@ def hist(self, x, bins=None, range=None, density=False, weights=None,
                 # set the top of this polygon
                 y[1:2*len(bins)-1:2], y[2:2*len(bins):2] = (m + bottom,
                                                             m + bottom)
-                if log:
-                    y[y < minimum] = minimum
                 if orientation == 'horizontal':
                     xvals.append(y.copy())
                     yvals.append(x.copy())
@@ -6809,9 +6762,9 @@ def hist(self, x, bins=None, range=None, density=False, weights=None,
             for patch_list in patches:
                 for patch in patch_list:
                     if orientation == 'vertical':
-                        patch.sticky_edges.y.append(minimum)
+                        patch.sticky_edges.y.append(0)
                     elif orientation == 'horizontal':
-                        patch.sticky_edges.x.append(minimum)
+                        patch.sticky_edges.x.append(0)
 
             # we return patches, so put it back in the expected order
             patches.reverse()

diff --git a/lib/matplotlib/tests/baseline_images/test_axes/hist_step_log_bottom.png b/lib/matplotlib/tests/baseline_images/test_axes/hist_step_log_bottom.png
diff --git a/lib/matplotlib/tests/baseline_images/test_axes/hist_steplog.pdf b/lib/matplotlib/tests/baseline_images/test_axes/hist_steplog.pdf
diff --git a/lib/matplotlib/tests/baseline_images/test_axes/hist_steplog.png b/lib/matplotlib/tests/baseline_images/test_axes/hist_steplog.png