{"id":3788,"date":"2024-04-07T10:44:33","date_gmt":"2024-04-07T03:44:33","guid":{"rendered":"https:\/\/www.sqlservertutorial.net\/?page_id=3788"},"modified":"2024-04-07T15:46:27","modified_gmt":"2024-04-07T08:46:27","slug":"sql-server-log","status":"publish","type":"page","link":"https:\/\/www.sqlservertutorial.net\/sql-server-math-functions\/sql-server-log\/","title":{"rendered":"SQL Server LOG() Function"},"content":{"rendered":"\n<p><strong>Summary<\/strong>: in this tutorial, you will learn how to use the SQL Server <code>LOG()<\/code> function to calculate the natural logarithm of a number.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id='introduction-to-sql-server-log-function'>Introduction to SQL Server LOG() function <a href=\"#introduction-to-sql-server-log-function\" class=\"anchor\" id=\"introduction-to-sql-server-log-function\" title=\"Anchor for Introduction to SQL Server LOG() function\">#<\/a><\/h2>\n\n\n\n<p>The natural logarithm is the logarithm to the base e, where e approximately equals <code>2.718<\/code>. In the SQL server, you can use the <code>LOG()<\/code> function to calculate the natural logarithm of a specified number.<\/p>\n\n\n\n<p>Here&#8217;s the syntax of the <code>LOG()<\/code> function:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-1\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\">LOG(n &#91;, base])<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-1\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>In this syntax:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>n<\/code> is a float or a value that can implicitly converted to a float.<\/li>\n\n\n\n<li><code>base<\/code> specifies the base for the logarithm. It is optional and defaults to e.<\/li>\n<\/ul>\n\n\n\n<p>The function returns <code>NULL<\/code> if either n or base is <code>NULL<\/code>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id='sql-server-log-function-examples'>SQL Server LOG() function examples <a href=\"#sql-server-log-function-examples\" class=\"anchor\" id=\"sql-server-log-function-examples\" title=\"Anchor for SQL Server LOG() function examples\">#<\/a><\/h2>\n\n\n\n<p>Let&#8217;s take some examples of using the <code>LOG()<\/code> function.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id='1-basic-sql-server-log-function-examples'>1) Basic SQL Server LOG() function examples <a href=\"#1-basic-sql-server-log-function-examples\" class=\"anchor\" id=\"1-basic-sql-server-log-function-examples\" title=\"Anchor for 1) Basic SQL Server LOG() function examples\">#<\/a><\/h3>\n\n\n\n<p>The following example uses the <code>LOG()<\/code> function to calculate the natural logarithm of 1:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-2\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span> <span class=\"hljs-keyword\">LOG<\/span>(<span class=\"hljs-number\">1<\/span>);<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-2\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Output:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-3\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\">result\n<span class=\"hljs-comment\">------<\/span>\n0\n\n(1 row affected)<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-3\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>The following statement uses the <code>LOG()<\/code> function to calculate the natural logarithm of e:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-4\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span> <span class=\"hljs-keyword\">LOG<\/span>(<span class=\"hljs-keyword\">EXP<\/span>(<span class=\"hljs-number\">1<\/span>)) <span class=\"hljs-keyword\">result<\/span>;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-4\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Output:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-5\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\">result\n<span class=\"hljs-comment\">-------<\/span>\n1<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-5\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>The following example calculates the natural logarithm of the number 10:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-6\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span> <span class=\"hljs-keyword\">LOG<\/span>(<span class=\"hljs-number\">10<\/span>) <span class=\"hljs-keyword\">result<\/span>;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-6\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Output:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-7\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\">result\n<span class=\"hljs-comment\">----------------<\/span>\n2.30258509299405<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-7\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>The following example uses the <code>LOG()<\/code> function to calculate the logarithm of 8 with base 3:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-8\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span> <span class=\"hljs-keyword\">LOG<\/span>(<span class=\"hljs-number\">8<\/span>,<span class=\"hljs-number\">2<\/span>) <span class=\"hljs-keyword\">result<\/span>;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-8\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Output:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-9\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\">result\n<span class=\"hljs-comment\">------<\/span>\n3<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-9\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<h3 class=\"wp-block-heading\" id='2-using-log-function-to-calculate-compound-interest'>2) Using LOG() function to calculate compound interest <a href=\"#2-using-log-function-to-calculate-compound-interest\" class=\"anchor\" id=\"2-using-log-function-to-calculate-compound-interest\" title=\"Anchor for 2) Using LOG() function to calculate compound interest\">#<\/a><\/h3>\n\n\n\n<p>Suppose you have an initial value <code>P<\/code>, the annual interest rate is<code> r%<\/code> per year, after <code>n<\/code> year, you&#8217;ll receive <code>F<\/code> amount.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After one year, you&#8217;ll receive F  = P(1 + r)<\/li>\n\n\n\n<li>After two years, you&#8217;ll receive F = P(1+ r) (1+r) = P (1+ r)<sup>2<\/sup><\/li>\n\n\n\n<li>After n years, you&#8217;ll receive F = P (1 + r)<sup>n<\/sup><\/li>\n<\/ul>\n\n\n\n<p>If you have 1000 <code>USD<\/code>, the annual interest rate is 5%, and if you want to receive 2000, you&#8217;ll have to wait for n  years, where n is: n = log(F\/P) \/ log(1 +r) = log(<code>1.5<\/code>)\/log(<code>1.05<\/code>) ~ <code>8.31<\/code> years.<\/p>\n\n\n\n<p>In SQL server, you can use the <code>LOG<\/code> function to do it:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-10\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">DECLARE<\/span> @p <span class=\"hljs-built_in\">decimal<\/span> = <span class=\"hljs-number\">1000<\/span>;\n<span class=\"hljs-keyword\">DECLARE<\/span> @f <span class=\"hljs-built_in\">decimal<\/span> = <span class=\"hljs-number\">1500<\/span>;\n<span class=\"hljs-keyword\">DECLARE<\/span> @r <span class=\"hljs-built_in\">decimal<\/span> = <span class=\"hljs-number\">5<\/span>; \n<span class=\"hljs-keyword\">DECLARE<\/span> @n <span class=\"hljs-built_in\">decimal<\/span>(<span class=\"hljs-number\">5<\/span>,<span class=\"hljs-number\">2<\/span>);\n\n<span class=\"hljs-keyword\">SET<\/span> @n = <span class=\"hljs-keyword\">LOG<\/span>(@f\/@p)\/ <span class=\"hljs-keyword\">LOG<\/span>(<span class=\"hljs-number\">1<\/span> + @r\/<span class=\"hljs-number\">100<\/span>);\n\n<span class=\"hljs-keyword\">SELECT<\/span> @n <span class=\"hljs-keyword\">years<\/span>;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-10\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Output:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-11\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\">years\n<span class=\"hljs-comment\">------<\/span>\n8.31<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-11\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<h3 class=\"wp-block-heading\" id='3-using-log-function-with-table-data'>3) Using LOG() function with table data <a href=\"#3-using-log-function-with-table-data\" class=\"anchor\" id=\"3-using-log-function-with-table-data\" title=\"Anchor for 3) Using LOG() function with table data\">#<\/a><\/h3>\n\n\n\n<p>First, <a href=\"https:\/\/www.sqlservertutorial.net\/sql-server-basics\/sql-server-create-table\/\">create a new table<\/a> called <code>investments<\/code> to store the present value, future value, and average annual interest rate:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-12\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">CREATE<\/span> <span class=\"hljs-keyword\">TABLE<\/span> investments (\n    <span class=\"hljs-keyword\">id<\/span> <span class=\"hljs-built_in\">INT<\/span> <span class=\"hljs-keyword\">IDENTITY<\/span> PRIMARY <span class=\"hljs-keyword\">KEY<\/span>,\n    present_value <span class=\"hljs-built_in\">DECIMAL<\/span>(<span class=\"hljs-number\">19<\/span>, <span class=\"hljs-number\">2<\/span>) <span class=\"hljs-keyword\">NOT<\/span> <span class=\"hljs-literal\">NULL<\/span>,\n    future_value <span class=\"hljs-built_in\">DECIMAL<\/span>(<span class=\"hljs-number\">19<\/span>, <span class=\"hljs-number\">2<\/span>) <span class=\"hljs-keyword\">NOT<\/span> <span class=\"hljs-literal\">NULL<\/span>,\n    annual_interest_rate <span class=\"hljs-built_in\">DECIMAL<\/span>(<span class=\"hljs-number\">19<\/span>, <span class=\"hljs-number\">2<\/span>) <span class=\"hljs-keyword\">NOT<\/span> <span class=\"hljs-literal\">NULL<\/span>\n);<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-12\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Second, <a href=\"https:\/\/www.sqlservertutorial.net\/sql-server-basics\/sql-server-insert-multiple-rows\/\">insert some rows<\/a> into the <code>investments<\/code> table:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-13\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">INSERT<\/span> <span class=\"hljs-keyword\">INTO<\/span>\n  investments (present_value, future_value, annual_interest_rate)\n<span class=\"hljs-keyword\">VALUES<\/span>\n  (<span class=\"hljs-number\">1000<\/span>, <span class=\"hljs-number\">1500<\/span>, <span class=\"hljs-number\">0.05<\/span>),\n  (<span class=\"hljs-number\">2000<\/span>, <span class=\"hljs-number\">5000<\/span>, <span class=\"hljs-number\">0.06<\/span>),\n  (<span class=\"hljs-number\">5000<\/span>, <span class=\"hljs-number\">10000<\/span>, <span class=\"hljs-number\">0.1<\/span>);<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-13\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Third, retrieve data from the <code>investments<\/code> table:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-14\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span> * <span class=\"hljs-keyword\">FROM<\/span> investments;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-14\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Finally, calculate the years to take to receive the future value from the present value and the annual interest rate:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-15\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span>\n  <span class=\"hljs-keyword\">id<\/span>,\n  present_value,\n  future_value,\n  annual_interest_rate,\n  <span class=\"hljs-keyword\">CAST<\/span>(\n    <span class=\"hljs-keyword\">ROUND<\/span>(\n      <span class=\"hljs-keyword\">LOG<\/span>(future_value \/ present_value) \/ <span class=\"hljs-keyword\">LOG<\/span>(<span class=\"hljs-number\">1<\/span> + annual_interest_rate),\n      <span class=\"hljs-number\">2<\/span>\n    ) <span class=\"hljs-keyword\">AS<\/span> <span class=\"hljs-built_in\">DEC<\/span> (<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">2<\/span>)\n  ) <span class=\"hljs-keyword\">years<\/span>\n<span class=\"hljs-keyword\">FROM<\/span>\n  investments;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-15\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Output:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-16\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\">id | present_value | future_value | annual_interest_rate | years\n<span class=\"hljs-comment\">---+---------------+--------------+----------------------+-------<\/span>\n1  | 1000.00       | 1500.00      | 0.05                 | 8.31\n2  | 2000.00       | 5000.00      | 0.06                 | 15.73\n3  | 5000.00       | 10000.00     | 0.10                 | 7.27\n(3 rows)<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-16\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<h2 class=\"wp-block-heading\" id='summary'>Summary <a href=\"#summary\" class=\"anchor\" id=\"summary\" title=\"Anchor for Summary\">#<\/a><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use the <code>LOG()<\/code> function to calculate the natural logarithm of a number.<\/li>\n<\/ul>\n<div class=\"helpful-block-content\" data-title=\"\">\n\t<header>\n\t\t<div class=\"wth-question\">Was this tutorial helpful?<\/div>\n\t\t<div class=\"wth-thumbs\">\n\t\t\t<button\n\t\t\t\tdata-post=\"3788\"\n\t\t\t\tdata-post-url=\"https:\/\/www.sqlservertutorial.net\/sql-server-math-functions\/sql-server-log\/\"\n\t\t\t\tdata-post-title=\"SQL Server LOG() Function\"\n\t\t\t\tdata-response=\"1\"\n\t\t\t\tclass=\"wth-btn-rounded wth-yes-btn\"\n\t\t\t>\n\t\t\t\t<svg\n\t\t\t\t\txmlns=\"http:\/\/www.w3.org\/2000\/svg\"\n\t\t\t\t\tviewBox=\"0 0 24 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