diff --git a/examples/projections/nongeo/cartesian.py b/examples/projections/nongeo/cartesian_linear.py
similarity index 94%
rename from examples/projections/nongeo/cartesian.py
rename to examples/projections/nongeo/cartesian_linear.py
index 9da8d2ebd81..c0b9df27c02 100644
--- a/examples/projections/nongeo/cartesian.py
+++ b/examples/projections/nongeo/cartesian_linear.py
@@ -1,6 +1,6 @@
 """
-Cartesian
-=========
+Cartesian linear
+================
 
 ``Xwidth/[height]``: Give the ``width`` of the figure and the optional argument ``height``.
 """
diff --git a/examples/projections/nongeo/cartesian_logarithmic.py b/examples/projections/nongeo/cartesian_logarithmic.py
new file mode 100644
index 00000000000..a5eb00513a7
--- /dev/null
+++ b/examples/projections/nongeo/cartesian_logarithmic.py
@@ -0,0 +1,37 @@
+"""
+Cartesian logarithmic
+=====================
+
+``xwidth[l]/[height[l]]``: Give the ``width`` of the figure and the optional argument \
+``height``. The axis or axes with a logarithmic transformation requires ``l`` after
+its size argument.
+"""
+import numpy as np
+import pygmt
+
+# Create a list of x values 0-100
+xline = np.arange(0, 101)
+# Create a list of y-values that are the square root of the x-values
+yline = xline ** 0.5
+# Create a list of x values for every 10 in 0-100
+xpoints = np.arange(0, 101, 10)
+# Create a list of y-values that are the square root of the x-values
+ypoints = xpoints ** 0.5
+
+fig = pygmt.Figure()
+fig.plot(
+    region=[1, 100, 0, 10],
+    # Set a logarithmic transformation on the x-axis
+    projection="X15cl/10c",
+    # Set the figures frame, color, and gridlines
+    frame=["WSne+gbisque", "x2g3", "ya2f1g2"],
+    x=xline,
+    y=yline,
+    # Set the line thickness to *1p*, the color to *blue*, and the style to *dash*
+    pen="1p,blue,-",
+)
+# Plot square root values as points on the line
+# Style of points is 0.3 cm square, color is *red* with a *black* outline
+# Points are not clipped if they go off the figure
+fig.plot(x=xpoints, y=ypoints, style="s0.3c", color="red", no_clip=True, pen="black")
+fig.show()
diff --git a/examples/projections/nongeo/cartesian_power.py b/examples/projections/nongeo/cartesian_power.py
new file mode 100644
index 00000000000..d3a9f01589b
--- /dev/null
+++ b/examples/projections/nongeo/cartesian_power.py
@@ -0,0 +1,34 @@
+"""
+Cartesian power
+===============
+
+**X**\ *width*\ [**p**\ *pvalue*]/[*height*\ [**p**\ *pvalue*]]: Give the
+*width* of the figure and the optional argument *height*. The axis or axes with a
+logarithmic transformation requires **p** and the power transformation for that axis.
+"""
+import numpy as np
+import pygmt
+
+# Create a list of y values 0-10
+yvalues = np.arange(0, 11)
+# Create a list of x-values that are the square of the y-values
+xvalues = yvalues ** 2
+
+fig = pygmt.Figure()
+fig.plot(
+    region=[0, 100, 0, 10],
+    # Set the power transformation of the x-axis, with a power of 0.5
+    projection="X15cp0.5/10c",
+    # Set the figures frame, color, and gridlines
+    frame=["WSne+givory", "xa1p", "ya2f1"],
+    # Set the line thickness to *thick*
+    # Use the default color *black* and the default style *solid*
+    pen="thick",
+    x=xvalues,
+    y=yvalues,
+)
+# Plot x,y values as points on the line
+# Style of points is 0.2 cm circles, color is *green* with a *black* outline
+# Points are not clipped if they go off the figure
+fig.plot(x=xvalues, y=yvalues, style="c0.2c", color="green", no_clip=True, pen="black")
+fig.show()