diff --git a/docs/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md b/docs/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
index 672fff70639fa..956bb891a0f02 100644
--- a/docs/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
+++ b/docs/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
@@ -12,7 +12,7 @@ Returns the logarithm of `x` based on base `b`.
 ## Syntax
 
 ```sql
-LOG(<b>,<x>)
+LOG(<b>[, <x>])
 ```
 
 ## Parameters
@@ -20,7 +20,7 @@ LOG(<b>,<x>)
 | Parameter | Description |
 |-----------|------------|
 | `<b>`     | Base should be greater than 0 and not be exactly 1.0 |
-| `<x>`     | Antilogarithm should be greater than 0 |
+| `<x>`     | optional, Antilogarithm should be greater than 0, default value is e |
 
 ## Return value
 
@@ -42,6 +42,18 @@ select log(5,1);
 +---------------+
 ```
 
+```sql
+select log(3),ln(3);
+```
+
+```text
++--------------------+--------------------+
+| log(3)             | ln(3)              |
++--------------------+--------------------+
+| 1.0986122886681098 | 1.0986122886681098 |
++--------------------+--------------------+
+```
+
 ```sql
 select log(3,20);
 ```
diff --git a/i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md b/i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
index a404eac5b2069..ef89e2c9b478a 100644
--- a/i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
+++ b/i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
@@ -12,7 +12,7 @@
 ## 语法
 
 ```sql
-LOG(<b>,<x>)
+LOG(<b>[, <x>])
 ```
 
 ## 参数
@@ -20,7 +20,7 @@ LOG(<b>,<x>)
 | 参数    | 说明 |
 |-------| -- |
 | `<b>` | 底数 必须大于 0 且不等于 1 |
-| `<x>` | 真数 必须大于 0         |
+| `<x>` | 可选，真数必须大于 0，默认为自然数e |
 
 ## 返回值
 
@@ -42,6 +42,18 @@ select log(5,1);
 +---------------+
 ```
 
+```sql
+select log(3),ln(3);
+```
+
+```text
++--------------------+--------------------+
+| log(3)             | ln(3)              |
++--------------------+--------------------+
+| 1.0986122886681098 | 1.0986122886681098 |
++--------------------+--------------------+
+```
+
 ```sql
 select log(3,20);
 ```
diff --git a/i18n/zh-CN/docusaurus-plugin-content-docs/version-3.0/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md b/i18n/zh-CN/docusaurus-plugin-content-docs/version-3.0/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
index a404eac5b2069..ef89e2c9b478a 100644
--- a/i18n/zh-CN/docusaurus-plugin-content-docs/version-3.0/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
+++ b/i18n/zh-CN/docusaurus-plugin-content-docs/version-3.0/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
@@ -12,7 +12,7 @@
 ## 语法
 
 ```sql
-LOG(<b>,<x>)
+LOG(<b>[, <x>])
 ```
 
 ## 参数
@@ -20,7 +20,7 @@ LOG(<b>,<x>)
 | 参数    | 说明 |
 |-------| -- |
 | `<b>` | 底数 必须大于 0 且不等于 1 |
-| `<x>` | 真数 必须大于 0         |
+| `<x>` | 可选，真数必须大于 0，默认为自然数e |
 
 ## 返回值
 
@@ -42,6 +42,18 @@ select log(5,1);
 +---------------+
 ```
 
+```sql
+select log(3),ln(3);
+```
+
+```text
++--------------------+--------------------+
+| log(3)             | ln(3)              |
++--------------------+--------------------+
+| 1.0986122886681098 | 1.0986122886681098 |
++--------------------+--------------------+
+```
+
 ```sql
 select log(3,20);
 ```
diff --git a/sidebars.json b/sidebars.json
index ece1a91c27bb6..57fad9e0575eb 100644
--- a/sidebars.json
+++ b/sidebars.json
@@ -1711,6 +1711,7 @@
                             "type": "category",
                             "label": "Analytic (Window) Functions",
                             "items": [
+                                "sql-manual/sql-functions/window-functions/overview",
                                 "sql-manual/sql-functions/window-functions/cume-dist",
                                 "sql-manual/sql-functions/window-functions/dense-rank",
                                 "sql-manual/sql-functions/window-functions/first-value",
@@ -1718,10 +1719,71 @@
                                 "sql-manual/sql-functions/window-functions/last-value",
                                 "sql-manual/sql-functions/window-functions/lead",
                                 "sql-manual/sql-functions/window-functions/ntile",
-                                "sql-manual/sql-functions/window-functions/overview",
                                 "sql-manual/sql-functions/window-functions/percent-rank",
                                 "sql-manual/sql-functions/window-functions/rank",
-                                "sql-manual/sql-functions/window-functions/row-number"
+                                "sql-manual/sql-functions/window-functions/row-number",
+                                "sql-manual/sql-functions/window-functions/any-value",
+                                "sql-manual/sql-functions/window-functions/approx-count-distinct",
+                                "sql-manual/sql-functions/window-functions/approx-top-k",
+                                "sql-manual/sql-functions/window-functions/approx-top-sum",
+                                "sql-manual/sql-functions/window-functions/array-agg",
+                                "sql-manual/sql-functions/window-functions/avg",
+                                "sql-manual/sql-functions/window-functions/avg-weighted",
+                                "sql-manual/sql-functions/window-functions/bitmap-agg",
+                                "sql-manual/sql-functions/window-functions/bitmap-intersect",
+                                "sql-manual/sql-functions/window-functions/bitmap-union",
+                                "sql-manual/sql-functions/window-functions/bitmap-union-count",
+                                "sql-manual/sql-functions/window-functions/bitmap-union-int",
+                                "sql-manual/sql-functions/window-functions/collect-list",
+                                "sql-manual/sql-functions/window-functions/collect-set",
+                                "sql-manual/sql-functions/window-functions/corr",
+                                "sql-manual/sql-functions/window-functions/count",
+                                "sql-manual/sql-functions/window-functions/count-by-enum",
+                                "sql-manual/sql-functions/window-functions/covar",
+                                "sql-manual/sql-functions/window-functions/covar-samp",
+                                "sql-manual/sql-functions/window-functions/group-array-intersect",
+                                "sql-manual/sql-functions/window-functions/group-bit-and",
+                                "sql-manual/sql-functions/window-functions/group-bit-or",
+                                "sql-manual/sql-functions/window-functions/group-bit-xor",
+                                "sql-manual/sql-functions/window-functions/group-bitmap-xor",
+                                "sql-manual/sql-functions/window-functions/group-concat",
+                                "sql-manual/sql-functions/window-functions/grouping",
+                                "sql-manual/sql-functions/window-functions/grouping-id",
+                                "sql-manual/sql-functions/window-functions/histogram",
+                                "sql-manual/sql-functions/window-functions/hll-raw-agg",
+                                "sql-manual/sql-functions/window-functions/hll-union-agg",
+                                "sql-manual/sql-functions/window-functions/intersect-count",
+                                "sql-manual/sql-functions/window-functions/kurt",
+                                "sql-manual/sql-functions/window-functions/linear-histogram",
+                                "sql-manual/sql-functions/window-functions/map-agg",
+                                "sql-manual/sql-functions/window-functions/max",
+                                "sql-manual/sql-functions/window-functions/max-by",
+                                "sql-manual/sql-functions/window-functions/median",
+                                "sql-manual/sql-functions/window-functions/min",
+                                "sql-manual/sql-functions/window-functions/min-by",
+                                "sql-manual/sql-functions/window-functions/percentile",
+                                "sql-manual/sql-functions/window-functions/percentile-approx",
+                                "sql-manual/sql-functions/window-functions/percentile-array",
+                                "sql-manual/sql-functions/window-functions/percentile_approx_weighted",
+                                "sql-manual/sql-functions/window-functions/quantile-union",
+                                "sql-manual/sql-functions/window-functions/regr-intercept",
+                                "sql-manual/sql-functions/window-functions/regr-slope",
+                                "sql-manual/sql-functions/window-functions/regr_intercept",
+                                "sql-manual/sql-functions/window-functions/regr_slope",
+                                "sql-manual/sql-functions/window-functions/retention",
+                                "sql-manual/sql-functions/window-functions/sequence-count",
+                                "sql-manual/sql-functions/window-functions/sequence-match",
+                                "sql-manual/sql-functions/window-functions/skew",
+                                "sql-manual/sql-functions/window-functions/stddev",
+                                "sql-manual/sql-functions/window-functions/stddev-samp",
+                                "sql-manual/sql-functions/window-functions/sum",
+                                "sql-manual/sql-functions/window-functions/sum0",
+                                "sql-manual/sql-functions/window-functions/topn",
+                                "sql-manual/sql-functions/window-functions/topn-array",
+                                "sql-manual/sql-functions/window-functions/topn-weighted",
+                                "sql-manual/sql-functions/window-functions/var-samp",
+                                "sql-manual/sql-functions/window-functions/variance",
+                                "sql-manual/sql-functions/window-functions/window-funnel"
                             ]
                         },
                         {
diff --git a/versioned_docs/version-3.0/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md b/versioned_docs/version-3.0/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
index 672fff70639fa..956bb891a0f02 100644
--- a/versioned_docs/version-3.0/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
+++ b/versioned_docs/version-3.0/sql-manual/sql-functions/scalar-functions/numeric-functions/log.md
@@ -12,7 +12,7 @@ Returns the logarithm of `x` based on base `b`.
 ## Syntax
 
 ```sql
-LOG(<b>,<x>)
+LOG(<b>[, <x>])
 ```
 
 ## Parameters
@@ -20,7 +20,7 @@ LOG(<b>,<x>)
 | Parameter | Description |
 |-----------|------------|
 | `<b>`     | Base should be greater than 0 and not be exactly 1.0 |
-| `<x>`     | Antilogarithm should be greater than 0 |
+| `<x>`     | optional, Antilogarithm should be greater than 0, default value is e |
 
 ## Return value
 
@@ -42,6 +42,18 @@ select log(5,1);
 +---------------+
 ```
 
+```sql
+select log(3),ln(3);
+```
+
+```text
++--------------------+--------------------+
+| log(3)             | ln(3)              |
++--------------------+--------------------+
+| 1.0986122886681098 | 1.0986122886681098 |
++--------------------+--------------------+
+```
+
 ```sql
 select log(3,20);
 ```