Scientific Logarithm Calculator
Common bases: 10 (Common), 2.718 (Natural), 2 (Binary)
Calculation Results:
Logbase(x) = –
Common Log (log10): –
Natural Log (ln): –
Error: Please ensure the number is greater than 0 and the base is greater than 0 and not equal to 1.
function calculateLogarithm() {
var x = parseFloat(document.getElementById('logValue').value);
var b = parseFloat(document.getElementById('logBase').value);
var resultArea = document.getElementById('logResultArea');
var errorArea = document.getElementById('logErrorArea');
// Validation
if (isNaN(x) || x <= 0 || isNaN(b) || b <= 0 || b === 1) {
resultArea.style.display = 'none';
errorArea.style.display = 'block';
return;
}
errorArea.style.display = 'none';
// Formula: log_b(x) = ln(x) / ln(b)
var customLog = Math.log(x) / Math.log(b);
var commonLog = Math.log10(x);
var naturalLog = Math.log(x);
document.getElementById('customLogResult').innerText = customLog.toFixed(6);
document.getElementById('commonLogResult').innerText = commonLog.toFixed(6);
document.getElementById('naturalLogResult').innerText = naturalLog.toFixed(6);
resultArea.style.display = 'block';
}
How to Use Logarithms on a Calculator
A logarithm is the inverse operation to exponentiation. It answers the question: "To what power must we raise the base to get this number?" While simple logs like log10(100) = 2 are easy to do mentally, complex values require a scientific calculator.
1. Understanding Calculator Keys
Most standard and scientific calculators feature two primary buttons for logarithms:
- LOG: This represents the common logarithm, which uses Base 10.
- LN: This represents the natural logarithm, which uses Base e (approximately 2.71828).
2. How to Solve Logs with Different Bases
If your calculator doesn't have a specific button for an arbitrary base (like Base 3 or Base 7), you must use the Change of Base Formula:
logb(x) = log(x) / log(b)
For example, to find log2(8):
- Type 8 and press the LOG button.
- Press the Divide (รท) button.
- Type 2 and press the LOG button.
- Press Enter (=). The result will be 3.
3. Practical Examples of Logarithms
| Application | Base Used | Example |
|---|---|---|
| pH Scale (Acidity) | Base 10 | -log[H+] |
| Richter Scale (Earthquakes) | Base 10 | M = log(A/A0) |
| Decibels (Sound) | Base 10 | 10 * log(P/P0) |
| Computer Science | Base 2 | Binary Search Steps |
Common Mistakes to Avoid
- Inputting Negative Numbers: Logarithms are only defined for positive numbers (x > 0). Attempting to log a negative number or zero will result in an "Error."
- Confusing Log and Ln: Ensure you are using the correct base. Using ln instead of log for a base-10 problem will give you the wrong answer.
- Base 1 Problems: The base (b) can never be 1, as 1 raised to any power remains 1.