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{
  "topic": "log-2",
  "input_types": [
    "int"
  ],
  "input_labels": [
    "n"
  ],
  "input_values": [
    "10"
  ],
  "type": "Calculate",
  "title": "Base-2 Logarithm",
  "category": "Arithmetic",
  "function": "function myFunc(arr) {\n        let n = arr[0];\n        return Math.log2(n);\n      }",
  "op_label": "Base-2 Logarithm, log<sub>2</sub>(n)",
  "explanation": "",
  "content": "<h2>Calculating the Base-2 Logarithm of a Number</h2>\n<p>The base-2 logarithm, also known as the binary logarithm, is a mathematical function denoted as \\(\\log_{2}(n)\\). It represents the power to which the base 2 must be raised to obtain the number \\(n\\). In other words, if \\(\\log_{2}(n) = x\\), then \\(2^x = n\\). This function is widely used in computer science, particularly in algorithms, data structures, and information theory, because of the binary nature of digital systems.</p>\n<p>The base-2 logarithm is especially useful for operations involving binary data or processes, as it directly relates to the concept of bits and binary growth. For example, the logarithm of 16 to base 2 is 4 because 2 raised to the power of 4 equals 16.</p>\n\n<h2>Examples</h2>\n<p>Let’s explore some examples to understand how to calculate the base-2 logarithm of a number.</p>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> Calculate the base-2 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 base-2 logarithm of 10:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{2}(10)\\)</li>\n<li>The value is approximately 3.3219 because \\(2^{3.3219} \\approx 10\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-2 logarithm of 10 is approximately 3.3219.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> Calculate the base-2 logarithm of 32.</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): 32</li></ul>\n<p>Next, we calculate the base-2 logarithm of 32:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{2}(32)\\)</li>\n<li>The value is 5 because \\(2^5 = 32\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-2 logarithm of 32 is 5.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">3.</span> Determine the base-2 logarithm of 8.</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): 8</li></ul>\n<p>Next, we calculate the base-2 logarithm of 8:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{2}(8)\\)</li>\n<li>The value is 3 because \\(2^3 = 8\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-2 logarithm of 8 is 3.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">4.</span> Calculate the base-2 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 base-2 logarithm of 20:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{2}(20)\\)</li>\n<li>The value is approximately 4.3219 because \\(2^{4.3219} \\approx 20\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-2 logarithm of 20 is approximately 4.3219.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">5.</span> Calculate the base-2 logarithm of 1.</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): 1</li></ul>\n<p>Next, we calculate the base-2 logarithm of 1:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{2}(1)\\)</li>\n<li>The value is 0 because \\(2^0 = 1\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-2 logarithm of 1 is 0.</p></div>"
}