Finding the log button and entering a logarithm

Most scientific calculators have a LOG button that calculates the base-10 logarithm of a number. To use it, type the number you want the logarithm of, then press LOG. The calculator will display the result. For example, to find log(100), you type 100, press LOG, and the calculator shows 2 (because 10² = 100).

On some calculators, especially older models, you may need to press LOG first, then type the number, then press equals. Check your calculator's manual or try both ways to see which works for yours. The order matters because different calculators follow different logic systems.

If your calculator has a small display screen, you may see "log(" appear on the screen after you press the button. This tells you the calculator is waiting for you to type the number. Type it, then press the closing parenthesis or equals to get your answer.

Key Takeaways

  • The LOG button on a scientific calculator finds the base-10 logarithm, which is the power you raise 10 to in order to get your original number.
  • Most calculators use the order: type number, press LOG, read the result — but some older models work the opposite way.
  • If your calculator has a natural logarithm button labeled LN, that calculates logarithms using the number e (about 2.718) as the base instead of 10.
  • Graphing calculators and phone calculator apps usually require you to type the function name or symbol before the number, such as log(100).

Understanding base-10 versus natural logarithms

A logarithm answers the question: what power do I raise this base to in order to get this number? The LOG button uses base 10, which is the most common logarithm in everyday math and science. When you see "log" written without a base number, it almost always means base 10.

Your calculator may also have an LN button, which stands for natural logarithm. This uses a special number called e (approximately 2.718) as the base instead of 10. Natural logarithms appear in advanced math, physics, and chemistry. If you need a base-10 logarithm, use LOG. If you need a natural logarithm, use LN. They give different answers for the same input number.

For example, log(100) = 2, but ln(100) ≈ 4.6. Both are correct — they just answer different questions. The LOG button is what you want for most everyday calculations.

Entering logarithms on a graphing calculator or phone

Graphing calculators and phone calculator apps work differently than basic scientific calculators. Instead of pressing a button after typing the number, you usually type the function name or symbol first. On a graphing calculator, you might type LOG(100) or log(100), then press ENTER. On a phone, you may need to switch to scientific mode to see the LOG button, or you can type the calculation directly if the app supports it.

Some phone calculator apps show the function buttons only when you rotate your phone to landscape mode. If you do not see a LOG button in portrait mode, try rotating your phone. If the app still does not have a logarithm function, you may need to download a scientific calculator app from your phone's app store.

Online calculators and spreadsheet programs like Excel or Google Sheets use the format =LOG(number) or =LOG10(number) for base-10 logarithms. Type the formula into a cell, and the program calculates the result. Check your spreadsheet's help menu if you are unsure of the exact syntax.

What to do if your calculator does not have a LOG button

Basic four-function calculators (addition, subtraction, multiplication, division only) do not have a LOG button. If you have one of these, you have three options: upgrade to a scientific calculator, use a phone or computer calculator app, or use an online calculator website.

Scientific calculators are inexpensive — most cost between $10 and $30 — and are worth having if you do math regularly. If you only need logarithms occasionally, a free online calculator or your phone's built-in calculator app will work just as well. Search "logarithm calculator" in your web browser to find dozens of free options.

Common mistakes when using the LOG button

The most common mistake is pressing LOG on a number that is zero or negative. Logarithms of zero and negative numbers do not exist in regular math — your calculator will show an error message like "ERR" or "undefined." This is correct behavior. You can only take the logarithm of positive numbers.

Another mistake is forgetting which base you are using. If you press LN by accident when you meant to press LOG, your answer will be wrong. Double-check which button you pressed before you write down your answer. If your result seems too large or too small compared to what you expected, you may have used the wrong button.

A third mistake is entering the number in the wrong order. If your calculator requires you to press LOG first, typing the number first will not work. If you get a strange result, try reversing the order and see if that fixes it. Your calculator's manual will tell you the correct order for your specific model.

Using logarithms in real calculations

Logarithms appear in science, engineering, and finance. In science, they are used to measure things that span huge ranges, like the brightness of stars, the acidity of water (pH), or the strength of earthquakes (the Richter scale). In finance, they help calculate compound interest and investment growth over time.

For example, if you want to know how many years it takes for money to double at a certain interest rate, you use logarithms. If you are measuring sound levels in decibels or comparing the intensity of earthquakes, logarithms are the tool. Once you understand what a logarithm does — it tells you what power to raise a base to — using the LOG button becomes straightforward.

Checking your answer

To verify that your logarithm is correct, use the reverse operation: raise 10 to the power of your answer and see if you get back your original number. If log(100) = 2, then 10² should equal 100. Most calculators have a power button (often labeled ^ or x^y) that lets you check this way.

This reverse check is especially useful when you are learning, because it helps you catch mistakes before they affect your work. If your check does not work out, you either made an error with the LOG button or with the power button. Try both calculations again, slowly, and compare your results.

Frequently Asked Questions

What is the difference between LOG and LN?

LOG uses base 10, while LN uses base e (about 2.718). Base 10 is more common in everyday math and science. Base e appears in advanced math, physics, and natural growth calculations. Use LOG unless you specifically need natural logarithms.

Can I take the logarithm of a negative number?

No. Logarithms of negative numbers do not exist in regular math. Your calculator will show an error. You can only take the logarithm of positive numbers greater than zero.

Why does log(1) always equal 0?

Because 10⁰ = 1. A logarithm answers the question: what power do I raise the base to? Since any number raised to the power of 0 equals 1, the logarithm of 1 is always 0, no matter what base you use.

How do I calculate a logarithm with a base other than 10 or e?

Use the change of base formula: log base b of x = log(x) ÷ log(b). For example, to find log base 2 of 8, calculate log(8) ÷ log(2) on your calculator. This works because you can convert any logarithm into base 10 or base e.

What if my calculator shows a decimal answer when I expected a whole number?

Decimals are normal. Most logarithms produce decimal answers. For example, log(50) ≈ 1.699, not a whole number. Only certain numbers like 1, 10, 100, and 1000 produce whole number logarithms in base 10. If your answer seems very different from what you expected, check that you used the correct button and entered the number correctly.