diff --git a/cpp-ch/local-engine/Parser/scalar_function_parser/ln.cpp b/cpp-ch/local-engine/Parser/scalar_function_parser/ln.cpp
index 423adb92d01b..8d3a86d3938e 100644
--- a/cpp-ch/local-engine/Parser/scalar_function_parser/ln.cpp
+++ b/cpp-ch/local-engine/Parser/scalar_function_parser/ln.cpp
@@ -28,6 +28,7 @@ class FunctionParserLn : public FunctionParserLogBase
     static constexpr auto name = "log";
 
     String getName() const override { return name; }
+    String getCHFunctionName() const override { return "log"; }
     DB::Float64 getParameterLowerBoundValue() const override { return 0.0; }
 };
 
diff --git a/cpp-ch/local-engine/Parser/scalar_function_parser/log10.cpp b/cpp-ch/local-engine/Parser/scalar_function_parser/log10.cpp
index fade79ace895..9c476c8d7760 100644
--- a/cpp-ch/local-engine/Parser/scalar_function_parser/log10.cpp
+++ b/cpp-ch/local-engine/Parser/scalar_function_parser/log10.cpp
@@ -28,6 +28,7 @@ class FunctionParserLog10 : public FunctionParserLogBase
     static constexpr auto name = "log10";
 
     String getName() const override { return name; }
+    String getCHFunctionName() const override { return "log10"; }
     DB::Float64 getParameterLowerBoundValue() const override { return 0.0; }
 };
 
diff --git a/cpp-ch/local-engine/Parser/scalar_function_parser/log1p.cpp b/cpp-ch/local-engine/Parser/scalar_function_parser/log1p.cpp
index 8a877ef5e7a7..886fb1752448 100644
--- a/cpp-ch/local-engine/Parser/scalar_function_parser/log1p.cpp
+++ b/cpp-ch/local-engine/Parser/scalar_function_parser/log1p.cpp
@@ -28,6 +28,7 @@ class FunctionParserLog1p : public FunctionParserLogBase
     static constexpr auto name = "log1p";
 
     String getName() const override { return name; }
+    String getCHFunctionName() const override { return "log1p"; }
     DB::Float64 getParameterLowerBoundValue() const override { return -1.0; }
 };
 
diff --git a/cpp-ch/local-engine/Parser/scalar_function_parser/log2.cpp b/cpp-ch/local-engine/Parser/scalar_function_parser/log2.cpp
index 5f71f22cc62f..e51675632086 100644
--- a/cpp-ch/local-engine/Parser/scalar_function_parser/log2.cpp
+++ b/cpp-ch/local-engine/Parser/scalar_function_parser/log2.cpp
@@ -28,6 +28,7 @@ class FunctionParserLog2 : public FunctionParserLogBase
     static constexpr auto name = "log2";
 
     String getName() const override { return name; }
+    String getCHFunctionName() const override { return "log2"; }
     DB::Float64 getParameterLowerBoundValue() const override { return 0.0; }
 };
 
diff --git a/cpp-ch/local-engine/Parser/scalar_function_parser/logarithm.h b/cpp-ch/local-engine/Parser/scalar_function_parser/logarithm.h
index 1acd22d2c431..36e76dcaa9ad 100644
--- a/cpp-ch/local-engine/Parser/scalar_function_parser/logarithm.h
+++ b/cpp-ch/local-engine/Parser/scalar_function_parser/logarithm.h
@@ -26,18 +26,21 @@ namespace DB
 namespace ErrorCodes
 {
     extern const int NUMBER_OF_ARGUMENTS_DOESNT_MATCH;
+    extern const int ILLEGAL_TYPE_OF_ARGUMENT;
 }
 }
 
 namespace local_engine
 {
+template<typename FirstParameterDataType>
 class FunctionParserLogBase : public FunctionParser
 {
 public:
     explicit FunctionParserLogBase(SerializedPlanParser * plan_parser_) : FunctionParser(plan_parser_) {}
     ~FunctionParserLogBase() override = default;
 
-    virtual DB::Float64 getParameterLowerBoundValue() const { return 0.0; }
+    virtual Number getParameterLowerBoundValue() const { return 0.0; }
+    virtual DB::String getCHFunctionName() const { return "log" };
 
     const ActionsDAG::Node * parse(
         const substrait::Expression_ScalarFunction & substrait_func,
@@ -48,24 +51,22 @@ class FunctionParserLogBase : public FunctionParser
             if (x <= c)
                 null
             else
-                log(c)
+                log(x)
         */
         auto parsed_args = parseFunctionArguments(substrait_func, "", actions_dag);
         if (parsed_args.size() != 1)
             throw Exception(ErrorCodes::NUMBER_OF_ARGUMENTS_DOESNT_MATCH, "Function {} requires exactly one arguments", getName());
 
         const auto * arg_node = parsed_args[0];
-        const std::string function_name = getName();
-        const auto * log_node = toFunctionNode(actions_dag, function_name, {arg_node});
-
-        auto result_type = log_node->result_type;
-        auto nullable_result_type = makeNullable(result_type);
+        
+        const std::string ch_function_name = getCHFunctionName();
+        const auto * log_node = toFunctionNode(actions_dag, ch_function_name, {arg_node});
+        auto nullable_result_type = makeNullable(log_node->result_type);
 
         const auto * null_const_node = addColumnToActionsDAG(actions_dag, nullable_result_type, Field());
-        const auto * nullable_log_node = ActionsDAGUtil::convertNodeType(actions_dag, log_node, nullable_result_type->getName(), log_node->result_name);
-        const DB::Float64 lowerBound = getParameterLowerBoundValue();
+        const Number lowerBound = getParameterLowerBoundValue();
         const auto * le_node = toFunctionNode(actions_dag, "lessOrEquals", {arg_node, addColumnToActionsDAG(actions_dag, result_type, lowerBound)});
-        const auto * result_node = toFunctionNode(actions_dag, "if", {le_node, null_const_node, nullable_log_node});
+        const auto * result_node = toFunctionNode(actions_dag, "if", {le_node, null_const_node, log_node});
 
         return convertNodeTypeIfNeeded(substrait_func, result_node, actions_dag);
     }