How to Do Log on Calculator

Logarithm Calculator & Solver

Note: Use 'e' for natural log (approx 2.718)

Results will appear here

function calculateLogarithm() { var x = parseFloat(document.getElementById('logValue').value); var b = parseFloat(document.getElementById('logBase').value); var resultDisplay = document.getElementById('logResult'); if (isNaN(x) || x <= 0) { resultDisplay.innerHTML = "Error: Value (x) must be greater than 0"; resultDisplay.style.color = "#e74c3c"; return; } if (isNaN(b) || b 0 and not 1″; resultDisplay.style.color = "#e74c3c"; return; } var result = Math.log(x) / Math.log(b); resultDisplay.innerHTML = "log_{" + b + "}(" + x + ") = " + result.toFixed(6); resultDisplay.style.color = "#2c3e50"; } function calculateNaturalLog() { var x = parseFloat(document.getElementById('logValue').value); var resultDisplay = document.getElementById('logResult'); if (isNaN(x) || x <= 0) { resultDisplay.innerHTML = "Error: Value (x) must be greater than 0"; resultDisplay.style.color = "#e74c3c"; return; } var result = Math.log(x); resultDisplay.innerHTML = "ln(" + x + ") = " + result.toFixed(6); resultDisplay.style.color = "#2c3e50"; }

Logarithms are fundamental to algebra, calculus, and data science. However, looking at a scientific calculator can be intimidating if you don't know which buttons to press. This guide explains exactly how to calculate logs, whether you are using a physical calculator (like a TI-84 or Casio) or an online tool.

1. Understanding the Buttons

Most calculators have two specific buttons dedicated to logarithms:

• LOG: This is the Common Logarithm. It always assumes a base of 10. For example, pressing "log 100" calculates log₁₀(100), which equals 2.
• LN: This is the Natural Logarithm. It assumes a base of e (Euler's number, approximately 2.718). It is used extensively in physics and finance.

2. How to Calculate a Log with a Custom Base

What if you need to find log₂(8)? Most standard calculators do not have a "log base 2" button. To solve this, you must use the Change of Base Formula:

log_b(x) = log(x) / log(b)

Example: How to do log₂ 8 on a calculator:

1. Type the "log" button.
2. Type "8" and close the parenthesis.
3. Press the divide (÷) button.
4. Type the "log" button again.
5. Type "2" and close the parenthesis.
6. Press enter. The result will be 3.

3. Step-by-Step for Different Calculator Types

On a TI-84 Plus / Graphing Calculator

Modern graphing calculators often have a shortcut. Press the ALPHA button, then WINDOW, and select 5: logBASE(. This allows you to input the base and the value directly without using the change of base formula.

On an iPhone or Smartphone

Open your calculator app and turn your phone sideways to reveal the scientific mode. You will see the "log₁₀" and "ln" buttons. Note: On some iPhones, you must enter the number first and then press the "log" button.

4. Common Logarithm Examples

Operation	Input Method	Result
Common Log of 1,000	log(1000)	3
Natural Log of 1	ln(1)	0
Log Base 2 of 16	log(16) / log(2)	4

Frequently Asked Questions

Why do I get an "Error" on my calculator?
Logarithms are only defined for positive numbers. If you try to calculate the log of 0 or a negative number, your calculator will return an error because there is no power you can raise a positive base to that results in a negative value.

What is the difference between Log and Ln?
"Log" usually refers to base 10 (common log), used for things like the Richter scale or pH levels. "Ln" is base e (2.718…), used for continuous growth calculations and complex math.