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1. Convert Online
2. Mathematics
3. Arithmetic
4. Natural Logarithm

{
  "topic": "log-e",
  "input_types": [
    "int"
  ],
  "input_labels": [
    "n"
  ],
  "input_values": [
    "10"
  ],
  "type": "Calculate",
  "title": "Natural Logarithm",
  "category": "Arithmetic",
  "function": "function myFunc(arr) {\n        let n = arr[0];\n        return Math.log(n);\n      }",
  "op_label": "Natural Logarithm log<sub>e</sub>(n)",
  "explanation": "",
  "content": "<h2>Calculating the Natural Logarithm of a Number</h2>\n<p>The natural logarithm, denoted as \\(\\log_{e}(n)\\) or simply \\(\\ln(n)\\), is a logarithm with base \\(e\\), where \\(e\\) is an irrational constant approximately equal to 2.71828. The natural logarithm is widely used in mathematics, particularly in calculus, and has applications in fields such as physics, engineering, and finance. It represents the power to which \\(e\\) must be raised to obtain the number \\(n\\). In other words, if \\(\\ln(n) = x\\), then \\(e^x = n\\).</p>\n\n<h2>Examples</h2>\n<p>Let’s explore some examples to understand how to calculate the natural logarithm of a number.</p>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> Calculate the natural logarithm of 10.</h3><h4 class=\"answer\">Answer</h4>\n<p>First, we identify the given number:</p>\n<p><b>Given:</b></p><ul><li>Number (n): 10</li></ul>\n<p>Next, we calculate the natural logarithm of 10:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\ln(10)\\)</li>\n<li>The value is approximately 2.3026 because \\(e^{2.3026} \\approx 10\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The natural logarithm of 10 is approximately 2.3026.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> Calculate the natural logarithm of 20.</h3><h4 class=\"answer\">Answer</h4>\n<p>We start by identifying the given number:</p>\n<p><b>Given:</b></p><ul><li>Number (n): 20</li></ul>\n<p>Next, we calculate the natural logarithm of 20:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\ln(20)\\)</li>\n<li>The value is approximately 2.9957 because \\(e^{2.9957} \\approx 20\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The natural logarithm of 20 is approximately 2.9957.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">3.</span> Determine the natural logarithm of 1.</h3><h4 class=\"answer\">Answer</h4>\n<p>First, we identify the given number:</p>\n<p><b>Given:</b></p><ul><li>Number (n): 1</li></ul>\n<p>Next, we calculate the natural logarithm of 1:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\ln(1)\\)</li>\n<li>The value is 0 because \\(e^0 = 1\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The natural logarithm of 1 is 0.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">4.</span> Calculate the natural logarithm of 100.</h3><h4 class=\"answer\">Answer</h4>\n<p>We start by identifying the given number:</p>\n<p><b>Given:</b></p><ul><li>Number (n): 100</li></ul>\n<p>Next, we calculate the natural logarithm of 100:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\ln(100)\\)</li>\n<li>The value is approximately 4.6052 because \\(e^{4.6052} \\approx 100\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The natural logarithm of 100 is approximately 4.6052.</p></div>"
}