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1. Convert Online
2. Mathematics
3. Arithmetic
4. Base-10 Logarithm

{
  "topic": "log-10",
  "input_types": [
    "int"
  ],
  "input_labels": [
    "n"
  ],
  "input_values": [
    "10"
  ],
  "type": "Calculate",
  "title": "Base-10 Logarithm",
  "category": "Arithmetic",
  "function": "function myFunc(arr) {\n        let n = arr[0];\n        return Math.log10(n);\n      }",
  "op_label": "Base-10 Logarithm, log<sub>10</sub>(n)",
  "explanation": "",
  "content": "<h2>Calculating the Base-10 Logarithm of a Number</h2>\n<p>The base-10 logarithm, also known as the common logarithm, is a mathematical function denoted as \\(\\log_{10}(n)\\). It represents the power to which the base 10 must be raised to obtain the number \\(n\\). In other words, if \\(\\log_{10}(n) = x\\), then \\(10^x = n\\). This function is widely used in various fields such as science, engineering, and finance.</p>\n<p>The base-10 logarithm is particularly useful for dealing with large numbers, compressing them into smaller, more manageable values. For example, the logarithm of 1000 to base 10 is 3 because 10 raised to the power of 3 equals 1000.</p>\n\n<h2>Examples</h2>\n<p>Let’s explore some examples to understand how to calculate the base-10 logarithm of a number.</p>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> Calculate the base-10 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-10 logarithm of 10:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{10}(10)\\)</li>\n<li>The value is 1 because \\(10^1 = 10\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-10 logarithm of 10 is 1.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> Calculate the base-10 logarithm of 25.</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): 25</li></ul>\n<p>Next, we calculate the base-10 logarithm of 25:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{10}(25)\\)</li>\n<li>The value is approximately 1.3979 because \\(10^{1.3979} \\approx 25\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-10 logarithm of 25 is approximately 1.3979.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">3.</span> Determine the base-10 logarithm of 1000.</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): 1000</li></ul>\n<p>Next, we calculate the base-10 logarithm of 1000:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{10}(1000)\\)</li>\n<li>The value is 3 because \\(10^3 = 1000\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-10 logarithm of 1000 is 3.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">4.</span> Calculate the base-10 logarithm of 50.</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): 50</li></ul>\n<p>Next, we calculate the base-10 logarithm of 50:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{10}(50)\\)</li>\n<li>The value is approximately 1.6990 because \\(10^{1.6990} \\approx 50\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-10 logarithm of 50 is approximately 1.6990.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">5.</span> Calculate the base-10 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-10 logarithm of 1:</p>\n<p><b>Steps:</b></p><ul><li>\\(\\log_{10}(1)\\)</li>\n<li>The value is 0 because \\(10^0 = 1\\).</li></ul>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The base-10 logarithm of 1 is 0.</p></div>"
}