diff --git a/datafusion/functions/src/math/log.rs b/datafusion/functions/src/math/log.rs
index 11d76d8086be9..732cfff6cf053 100644
--- a/datafusion/functions/src/math/log.rs
+++ b/datafusion/functions/src/math/log.rs
@@ -362,23 +362,27 @@ impl ScalarUDFImpl for LogFunc {
         } else {
             lit(ScalarValue::new_ten(&number_datatype)?)
         };
+        let base_nullable = info.nullable(&base)?;
 
         match number {
             Expr::Literal(value, _)
-                if value == ScalarValue::new_one(&number_datatype)? =>
+                if value == ScalarValue::new_one(&number_datatype)? && !base_nullable =>
             {
                 Ok(ExprSimplifyResult::Simplified(lit(ScalarValue::new_zero(
                     &info.get_data_type(&base)?,
                 )?)))
             }
             Expr::ScalarFunction(ScalarFunction { func, mut args })
-                if is_pow(&func) && args.len() == 2 && base == args[0] =>
+                if is_pow(&func)
+                    && args.len() == 2
+                    && base == args[0]
+                    && !base_nullable =>
             {
                 let b = args.pop().unwrap(); // length checked above
                 Ok(ExprSimplifyResult::Simplified(b))
             }
             number => {
-                if number == base {
+                if number == base && !base_nullable {
                     Ok(ExprSimplifyResult::Simplified(lit(ScalarValue::new_one(
                         &number_datatype,
                     )?)))
diff --git a/datafusion/functions/src/math/power.rs b/datafusion/functions/src/math/power.rs
index 54ba0d3581e3a..30ac401b5ff7d 100644
--- a/datafusion/functions/src/math/power.rs
+++ b/datafusion/functions/src/math/power.rs
@@ -140,6 +140,7 @@ impl ScalarUDFImpl for PowerFunc {
         let [base, exponent] = take_function_args("power", args)?;
         let base_type = info.get_data_type(&base)?;
         let exponent_type = info.get_data_type(&exponent)?;
+        let base_nullable = info.nullable(&base)?;
         let return_type =
             self.return_type(&[base_type.clone(), exponent_type.clone()])?;
 
@@ -167,7 +168,7 @@ impl ScalarUDFImpl for PowerFunc {
 
         match exponent {
             Expr::Literal(value, _)
-                if value == ScalarValue::new_zero(&exponent_type)? =>
+                if value == ScalarValue::new_zero(&exponent_type)? && !base_nullable =>
             {
                 Ok(ExprSimplifyResult::Simplified(lit(ScalarValue::new_one(
                     &return_type,
@@ -179,7 +180,10 @@ impl ScalarUDFImpl for PowerFunc {
                 )))
             }
             Expr::ScalarFunction(ScalarFunction { func, mut args })
-                if is_log(&func) && args.len() == 2 && base == args[0] =>
+                if is_log(&func)
+                    && args.len() == 2
+                    && base == args[0]
+                    && !base_nullable =>
             {
                 let b = args.pop().unwrap(); // length checked above
                 let b_type = info.get_data_type(&b)?;
diff --git a/datafusion/sqllogictest/test_files/math.slt b/datafusion/sqllogictest/test_files/math.slt
index 999709dfe77ea..b6bf51dd4799a 100644
--- a/datafusion/sqllogictest/test_files/math.slt
+++ b/datafusion/sqllogictest/test_files/math.slt
@@ -1182,6 +1182,55 @@ logical_plan
 02)--TableScan: aggregate_simple projection=[]
 physical_plan DataSourceExec: file_groups={1 group: [[WORKSPACE_ROOT/datafusion/core/tests/data/aggregate_simple.csv]]}, projection=[NULL as log(NULL,aggregate_simple.c2)], file_type=csv, has_header=true
 
+# Simplification must preserve NULLs from nullable columns
+query RRRRR rowsort
+SELECT
+  log(a, 1),
+  log(a, a),
+  log(a, power(a, b)),
+  power(a, 0),
+  power(a, log(a, b))
+FROM (VALUES (NULL::double, 2.0::double), (2.0, 3.0)) AS t(a, b);
+----
+0 1 3 1 3
+NULL NULL NULL NULL NULL
+
+# Nullable bases must remain in the optimized plan so they can propagate NULL
+query TT
+EXPLAIN SELECT
+  log(a, 1) AS l1,
+  log(a, a) AS la,
+  power(a, 0) AS p0,
+  power(a, log(a, b)) AS pl
+FROM (VALUES (NULL::double, 2.0::double), (2.0, 3.0)) AS t(a, b);
+----
+logical_plan
+01)Projection: log(t.a, Float64(1)) AS l1, log(t.a, t.a) AS la, power(t.a, Float64(0)) AS p0, power(t.a, log(t.a, t.b)) AS pl
+02)--SubqueryAlias: t
+03)----Projection: column1 AS a, column2 AS b
+04)------Values: (Float64(NULL) AS NULL, Float64(2)), (Float64(2), Float64(3))
+physical_plan
+01)ProjectionExec: expr=[log(column1@0, 1) as l1, log(column1@0, column1@0) as la, power(column1@0, 0) as p0, power(column1@0, log(column1@0, column2@1)) as pl]
+02)--DataSourceExec: partitions=1, partition_sizes=[1]
+
+# Non-nullable bases still use the existing simplifications
+query TT
+EXPLAIN SELECT
+  log(a, 1) AS l1,
+  log(a, a) AS la,
+  power(a, 0) AS p0,
+  power(a, log(a, b)) AS pl
+FROM (VALUES (2.0::double, 3.0::double)) AS t(a, b);
+----
+logical_plan
+01)Projection: Float64(0) AS l1, Float64(1) AS la, Float64(1) AS p0, t.b AS pl
+02)--SubqueryAlias: t
+03)----Projection: column2 AS b
+04)------Values: (Float64(2), Float64(3))
+physical_plan
+01)ProjectionExec: expr=[0 as l1, 1 as la, 1 as p0, column2@1 as pl]
+02)--DataSourceExec: partitions=1, partition_sizes=[1]
+
 # Float 16/32/64 for log
 query RT
 SELECT log(2.5, arrow_cast(10.9, 'Float16')), arrow_typeof(log(2.5, arrow_cast(10.9, 'Float16')));