diff --git a/python/pyspark/sql/functions.py b/python/pyspark/sql/functions.py
index 177fc196e083..acdb01d3d3f5 100644
--- a/python/pyspark/sql/functions.py
+++ b/python/pyspark/sql/functions.py
@@ -404,18 +404,23 @@ def when(condition, value):
     return Column(jc)
 
 
-@since(1.4)
-def log(col, base=math.e):
+@since(1.5)
+def log(arg1, arg2=None):
     """Returns the first argument-based logarithm of the second argument.
 
-    >>> df.select(log(df.age, 10.0).alias('ten')).map(lambda l: str(l.ten)[:7]).collect()
+    If there is only one argument, then this takes the natural logarithm of the argument.
+
+    >>> df.select(log(10.0, df.age).alias('ten')).map(lambda l: str(l.ten)[:7]).collect()
     ['0.30102', '0.69897']
 
     >>> df.select(log(df.age).alias('e')).map(lambda l: str(l.e)[:7]).collect()
     ['0.69314', '1.60943']
     """
     sc = SparkContext._active_spark_context
-    jc = sc._jvm.functions.log(base, _to_java_column(col))
+    if arg2 is None:
+        jc = sc._jvm.functions.log(_to_java_column(arg1))
+    else:
+        jc = sc._jvm.functions.log(arg1, _to_java_column(arg2))
     return Column(jc)
 
 
diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/math.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/math.scala
index 67cb0b508ca9..280258d69163 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/math.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/math.scala
@@ -258,6 +258,10 @@ case class Pow(left: Expression, right: Expression)
 
 case class Logarithm(left: Expression, right: Expression)
   extends BinaryMathExpression((c1, c2) => math.log(c2) / math.log(c1), "LOG") {
+
+  /**
+   * Natural log, i.e. using e as the base.
+   */
   def this(child: Expression) = {
     this(EulerNumber(), child)
   }