diff --git a/sqlglot/dialects/bigquery.py b/sqlglot/dialects/bigquery.py
index ba61cd1649..0dc14cf4e8 100644
--- a/sqlglot/dialects/bigquery.py
+++ b/sqlglot/dialects/bigquery.py
@@ -310,11 +310,12 @@ def _build_levenshtein(args: t.List) -> exp.Levenshtein:
 
 def _build_format_time(expr_type: t.Type[exp.Expression]) -> t.Callable[[t.List], exp.TimeToStr]:
     def _builder(args: t.List) -> exp.TimeToStr:
-        return exp.TimeToStr(
-            this=expr_type(this=seq_get(args, 1)),
-            format=seq_get(args, 0),
-            zone=seq_get(args, 2),
+        # "bigquery")(expr_type(... -> "bigquery")([expr_type(...])
+        formatted_time = build_formatted_time(exp.TimeToStr, "bigquery")(
+            [expr_type(this=seq_get(args, 1)), seq_get(args, 0)]
         )
+        formatted_time.set("zone", seq_get(args, 2))
+        return formatted_time
 
     return _builder
 
@@ -369,6 +370,7 @@ class BigQuery(Dialect):
 
     # https://cloud.google.com/bigquery/docs/reference/standard-sql/format-elements#format_elements_date_time
     TIME_MAPPING = {
+        "%x": "%m/%d/%y",
         "%D": "%m/%d/%y",
         "%E6S": "%S.%f",
         "%e": "%-d",
diff --git a/sqlglot/dialects/duckdb.py b/sqlglot/dialects/duckdb.py
index fe93eab251..b7e1b00f22 100644
--- a/sqlglot/dialects/duckdb.py
+++ b/sqlglot/dialects/duckdb.py
@@ -423,6 +423,7 @@ class DuckDB(Dialect):
         **Dialect.DATE_PART_MAPPING,
         "DAYOFWEEKISO": "ISODOW",
     }
+
     DATE_PART_MAPPING.pop("WEEKDAY")
 
     def to_json_path(self, path: t.Optional[exp.Expression]) -> t.Optional[exp.Expression]:
diff --git a/tests/dialects/test_bigquery.py b/tests/dialects/test_bigquery.py
index 08229ddb02..37976de3af 100644
--- a/tests/dialects/test_bigquery.py
+++ b/tests/dialects/test_bigquery.py
@@ -2897,8 +2897,8 @@ def test_format_temporal(self):
         self.validate_all(
             "SELECT FORMAT_DATETIME('%x', '2023-12-25 15:30:00')",
             write={
-                "bigquery": "SELECT FORMAT_DATETIME('%x', '2023-12-25 15:30:00')",
-                "duckdb": "SELECT STRFTIME(CAST('2023-12-25 15:30:00' AS TIMESTAMP), '%x')",
+                "bigquery": "SELECT FORMAT_DATETIME('%D', '2023-12-25 15:30:00')",
+                "duckdb": "SELECT STRFTIME(CAST('2023-12-25 15:30:00' AS TIMESTAMP), '%m/%d/%y')",
             },
         )
         self.validate_all(