diff --git a/datafusion/core/tests/sql/functions.rs b/datafusion/core/tests/sql/functions.rs
index 517e7f1863c7..de2b04ba34d3 100644
--- a/datafusion/core/tests/sql/functions.rs
+++ b/datafusion/core/tests/sql/functions.rs
@@ -610,3 +610,61 @@ async fn pi_function() -> Result<()> {
     assert_batches_eq!(expected, &actual);
     Ok(())
 }
+
+macro_rules! assert_logical_plan {
+    ($ctx:expr, $udf_call:expr, $expected:expr) => {{
+        let sql = format!("SELECT {}", $udf_call);
+        let logical_plan = $ctx.create_logical_plan(&sql)?;
+        let formatted = format!("{:?}", logical_plan);
+        assert_eq!($expected, formatted.split("\n").collect::<Vec<&str>>());
+    }};
+}
+
+#[tokio::test]
+async fn test_log_round_logical_plan() -> Result<()> {
+    let ctx = SessionContext::new();
+
+    assert_logical_plan!(
+        ctx,
+        "log(2.0, 2)",
+        vec!["Projection: log(Float64(2), Int64(2))", "  EmptyRelation",]
+    );
+
+    assert_logical_plan!(
+        ctx,
+        "log(2::Decimal(38,10), 2::Decimal(38,10))",
+        vec![
+            "Projection: log(CAST(Int64(2) AS Decimal(38, 10)), CAST(Int64(2) AS Decimal(38, 10)))",
+            "  EmptyRelation",
+        ]
+    );
+
+    assert_logical_plan!(
+        ctx,
+        "log(2::Decimal(38,10), 2)",
+        vec![
+            "Projection: log(CAST(Int64(2) AS Decimal(38, 10)), Int64(2))",
+            "  EmptyRelation",
+        ]
+    );
+
+    assert_logical_plan!(
+        ctx,
+        "round(5.7, 2)",
+        vec![
+            "Projection: round(Float64(5.7), Int64(2))",
+            "  EmptyRelation",
+        ]
+    );
+
+    assert_logical_plan!(
+        ctx,
+        "round(5.7::Decimal(38,10), 2)",
+        vec![
+            "Projection: round(CAST(Float64(5.7) AS Decimal(38, 10)), Int64(2))",
+            "  EmptyRelation",
+        ]
+    );
+
+    Ok(())
+}
diff --git a/datafusion/expr/src/function.rs b/datafusion/expr/src/function.rs
index e6cdfa428f7b..a3dad8f70dfc 100644
--- a/datafusion/expr/src/function.rs
+++ b/datafusion/expr/src/function.rs
@@ -559,6 +559,8 @@ pub fn signature(fun: &BuiltinScalarFunction) -> Signature {
                     DataType::Decimal(38, 10),
                     DataType::Decimal(38, 10),
                 ]),
+                TypeSignature::Exact(vec![DataType::Decimal(38, 10), DataType::Int64]),
+                TypeSignature::Exact(vec![DataType::Float64, DataType::Int64]),
             ],
             fun.volatility(),
         ),
@@ -567,6 +569,8 @@ pub fn signature(fun: &BuiltinScalarFunction) -> Signature {
                 TypeSignature::Exact(vec![DataType::Float64]),
                 TypeSignature::Exact(vec![DataType::Float32]),
                 // NOTE: stub, won't execute
+                TypeSignature::Exact(vec![DataType::Float64, DataType::Int64]),
+                TypeSignature::Exact(vec![DataType::Decimal(38, 10), DataType::Int64]),
                 TypeSignature::Exact(vec![DataType::Decimal(38, 10), DataType::Int32]),
             ],
             fun.volatility(),