Common log base is 10, Natural log base (e) is approx. 2.71828.
Result:
Calculation Steps:
function calculateLog() {
var x = parseFloat(document.getElementById('logValue').value);
var b = parseFloat(document.getElementById('logBase').value);
var resultDiv = document.getElementById('logResultWrapper');
var errorDiv = document.getElementById('logError');
var mainResult = document.getElementById('logMainResult');
var stepsDiv = document.getElementById('logSteps');
errorDiv.style.display = 'none';
resultDiv.style.display = 'none';
if (isNaN(x) || isNaN(b)) {
errorDiv.innerHTML = "Please enter valid numbers for both the value and the base.";
errorDiv.style.display = 'block';
return;
}
if (x <= 0) {
errorDiv.innerHTML = "The number (x) must be greater than 0.";
errorDiv.style.display = 'block';
return;
}
if (b <= 0 || b === 1) {
errorDiv.innerHTML = "The base (b) must be greater than 0 and not equal to 1.";
errorDiv.style.display = 'block';
return;
}
// Calculation using change of base formula: log_b(x) = ln(x) / ln(b)
var lnX = Math.log(x);
var lnB = Math.log(b);
var result = lnX / lnB;
var formattedResult = +result.toFixed(6);
mainResult.innerHTML = "log" + b + "(" + x + ") = " + formattedResult;
var stepsHtml = "";
stepsHtml += "Step 1: Use the Change of Base Formula:";
stepsHtml += "logb(x) = ln(x) / ln(b)";
stepsHtml += "Step 2: Plug in the values:";
stepsHtml += "log" + b + "(" + x + ") = ln(" + x + ") / ln(" + b + ")";
stepsHtml += "Step 3: Calculate natural logarithms:";
stepsHtml += "ln(" + x + ") ≈ " + lnX.toFixed(8) + "";
stepsHtml += "ln(" + b + ") ≈ " + lnB.toFixed(8) + "";
stepsHtml += "Step 4: Divide the results:";
stepsHtml += lnX.toFixed(8) + " / " + lnB.toFixed(8) + " = " + result.toFixed(10) + "";
stepsHtml += "Final Answer: " + formattedResult;
stepsDiv.innerHTML = stepsHtml;
resultDiv.style.display = 'block';
}
Understanding Logarithms and Their Calculation
A logarithm is the inverse operation to exponentiation. It essentially answers the question: "To what power must we raise a base (b) to get a specific number (x)?" This tool helps you solve that equation instantly while showing the mathematical logic involved.
The Logarithm Formula
The basic definition is:
logb(x) = y if and only if by = x
The Change of Base Formula
Since most calculators only have buttons for natural logs (base e) or common logs (base 10), mathematicians use the Change of Base Formula to solve logs with any base: