@@ -89,9 +89,9 @@ impl ScalarUDFImpl for LogFunc {
             (input[0].sort_properties, input[1].sort_properties)
         };
         match (num_sort_properties, base_sort_properties) {
-            (first @ SortProperties::Ordered(value), SortProperties::Ordered(base))
-                if !value.descending && base.descending
-                    || value.descending && !base.descending =>
+            (first @ SortProperties::Ordered(num), SortProperties::Ordered(base))
+                if num.descending != base.descending
+                    && num.nulls_first == base.nulls_first =>
             {
                 Ok(first)
             }
@@ -370,7 +370,7 @@ mod tests {
             assert_eq!(result, order.sort_properties);
         }
 
-        // Test log(base, num)
+        // Test log(base, num), where `nulls_first` is the same
         let mut results = Vec::with_capacity(orders.len() * orders.len());
         for base_order in orders.iter() {
             for num_order in orders.iter().cloned() {
@@ -430,5 +430,23 @@ mod tests {
             SortProperties::Singleton,
         ];
         assert_eq!(results, expected);
+
+        // Test with different `nulls_first`
+        let base_order = ExprProperties::new_unknown().with_order(
+            SortProperties::Ordered(SortOptions {
+                descending: true,
+                nulls_first: true,
+            }),
+        );
+        let num_order = ExprProperties::new_unknown().with_order(
+            SortProperties::Ordered(SortOptions {
+                descending: false,
+                nulls_first: false,
+            }),
+        );
+        assert_eq!(
+            log.output_ordering(&[base_order, num_order]).unwrap(),
+            SortProperties::Unordered
+        );
     }
 }
@@ -519,7 +519,7 @@ CREATE EXTERNAL TABLE aggregate_test_100 (
 )
 STORED AS CSV
 WITH ORDER(c11)
-WITH ORDER(c12 DESC)
+WITH ORDER(c12 DESC NULLS LAST)
 LOCATION '../../testing/data/csv/aggregate_test_100.csv'
 OPTIONS ('format.has_header' 'true');
 
@@ -566,22 +566,22 @@ physical_plan
 01)SortPreservingMergeExec: [log_c11_base_c12@0 ASC NULLS LAST]
 02)--ProjectionExec: expr=[log(c12@1, CAST(c11@0 AS Float64)) as log_c11_base_c12]
 03)----RepartitionExec: partitioning=RoundRobinBatch(4), input_partitions=1
-04)------CsvExec: file_groups={1 group: [[WORKSPACE_ROOT/testing/data/csv/aggregate_test_100.csv]]}, projection=[c11, c12], output_orderings=[[c11@0 ASC NULLS LAST], [c12@1 DESC]], has_header=true
+04)------CsvExec: file_groups={1 group: [[WORKSPACE_ROOT/testing/data/csv/aggregate_test_100.csv]]}, projection=[c11, c12], output_orderings=[[c11@0 ASC NULLS LAST], [c12@1 DESC NULLS LAST]], has_header=true
 
 query TT
 EXPLAIN SELECT LOG(c11, c12) as log_c12_base_c11
 FROM aggregate_test_100
-ORDER BY log_c12_base_c11 DESC;
+ORDER BY log_c12_base_c11 DESC NULLS LAST;
 ----
 logical_plan
-01)Sort: log_c12_base_c11 DESC NULLS FIRST
+01)Sort: log_c12_base_c11 DESC NULLS LAST
 02)--Projection: log(CAST(aggregate_test_100.c11 AS Float64), aggregate_test_100.c12) AS log_c12_base_c11
 03)----TableScan: aggregate_test_100 projection=[c11, c12]
 physical_plan
-01)SortPreservingMergeExec: [log_c12_base_c11@0 DESC]
+01)SortPreservingMergeExec: [log_c12_base_c11@0 DESC NULLS LAST]
 02)--ProjectionExec: expr=[log(CAST(c11@0 AS Float64), c12@1) as log_c12_base_c11]
 03)----RepartitionExec: partitioning=RoundRobinBatch(4), input_partitions=1
-04)------CsvExec: file_groups={1 group: [[WORKSPACE_ROOT/testing/data/csv/aggregate_test_100.csv]]}, projection=[c11, c12], output_orderings=[[c11@0 ASC NULLS LAST], [c12@1 DESC]], has_header=true
+04)------CsvExec: file_groups={1 group: [[WORKSPACE_ROOT/testing/data/csv/aggregate_test_100.csv]]}, projection=[c11, c12], output_orderings=[[c11@0 ASC NULLS LAST], [c12@1 DESC NULLS LAST]], has_header=true
 
 statement ok
 drop table aggregate_test_100;