diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
index f4dfec56659..405cea6b6a6 100644
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -3885,8 +3885,18 @@ numeric_log(PG_FUNCTION_ARGS)
 			PG_RETURN_NUMERIC(make_result(&const_zero));
 		}
 		Assert(NUMERIC_IS_PINF(num2));
-		/* log(finite-positive, Inf) is Inf */
-		PG_RETURN_NUMERIC(make_result(&const_pinf));
+
+		/*
+		 * For a finite-positive base, log(base, Inf) = Inf / ln(base), so the
+		 * sign depends on whether base is more or less than 1.  If base = 1,
+		 * fall through and let log_var report the error.
+		 */
+		init_var_from_num(num1, &arg1);
+		sign1 = cmp_var(&arg1, &const_one);
+		if (sign1 < 0)
+			PG_RETURN_NUMERIC(make_result(&const_ninf));
+		if (sign1 > 0)
+			PG_RETURN_NUMERIC(make_result(&const_pinf));
 	}
 
 	/*
@@ -10812,6 +10822,16 @@ log_var(const NumericVar *base, const NumericVar *num, NumericVar *result)
 	int			ln_base_rscale;
 	int			ln_num_rscale;
 
+	/*
+	 * ln_var will throw a suitable error for most invalid-input cases, but we
+	 * need a special case for base == 1, else we'd report "division by zero"
+	 * which is a bit confusing.
+	 */
+	if (cmp_var(base, &const_one) == 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
+				 errmsg("cannot take logarithm using base one")));
+
 	init_var(&ln_base);
 	init_var(&ln_num);
 
diff --git a/src/test/regress/expected/numeric.out b/src/test/regress/expected/numeric.out
index c58e232a263..fca2cb46c8c 100644
--- a/src/test/regress/expected/numeric.out
+++ b/src/test/regress/expected/numeric.out
@@ -933,6 +933,14 @@ FROM v AS v1(x1), v AS v2(x2);
       NaN |      NaN |                NaN
 (16 rows)
 
+SELECT log('0.5'::numeric, 'inf');
+    log    
+-----------
+ -Infinity
+(1 row)
+
+SELECT log('1'::numeric, 'inf');
+ERROR:  cannot take logarithm using base one
 SELECT log('0'::numeric, '10');
 ERROR:  cannot take logarithm of zero
 SELECT log('10'::numeric, '0');
@@ -3492,7 +3500,7 @@ ERROR:  cannot take logarithm of zero
 select log(12.34, 0.0);
 ERROR:  cannot take logarithm of zero
 select log(1.0, 12.34);
-ERROR:  division by zero
+ERROR:  cannot take logarithm using base one
 -- some random tests
 select log(1.23e-89, 6.4689e45);
                                               log                                               
diff --git a/src/test/regress/sql/numeric.sql b/src/test/regress/sql/numeric.sql
index 640c6d92f4c..5fd5c02f636 100644
--- a/src/test/regress/sql/numeric.sql
+++ b/src/test/regress/sql/numeric.sql
@@ -713,6 +713,8 @@ SELECT x1, x2,
   log(x1, x2)
 FROM v AS v1(x1), v AS v2(x2);
 
+SELECT log('0.5'::numeric, 'inf');
+SELECT log('1'::numeric, 'inf');
 SELECT log('0'::numeric, '10');
 SELECT log('10'::numeric, '0');
 SELECT log('-inf'::numeric, '10');