Finding the logarithm button on your calculator

Most scientific calculators have a LOG button that calculates the base-10 logarithm (also called the common logarithm). On some calculators it appears as "LOG" in white text on a colored key. On others it may be a secondary function accessed by pressing a shift or second-function key first, then LOG.

If your calculator has both LOG and LN buttons, LOG is base-10 and LN is the natural logarithm (base e). For everyday math and science classes, you will use LOG most often. Check your calculator's manual or the key labels to see which functions are primary (printed directly on the key) and which are secondary (printed above the key in smaller text).

Graphing calculators like the TI-84 also have a LOG function, usually found in the MATH menu under "NUM" or accessed directly from the home screen. Basic four-function calculators do not have a logarithm function at all.

Key Takeaways

  • The LOG button on a scientific calculator finds the base-10 logarithm; press the number first, then LOG, or LOG first depending on your calculator model.
  • If LOG is printed above the key in smaller text, you must press a Shift or 2nd key before pressing LOG.
  • LN calculates the natural logarithm (base e), which is different from LOG and used in different contexts.
  • Basic calculators without a scientific mode do not have logarithm functions; you need a scientific or graphing calculator.

The order of buttons matters: number first or function first

On most modern scientific calculators, you enter the number first, then press LOG. For example, to find the logarithm of 100, you would press 1, 0, 0, then LOG. The answer 2 appears on the display (because 10² = 100).

On some older calculators, particularly those with Reverse Polish Notation (RPN), you press LOG first, then the number. Your calculator's manual will tell you which order it uses. If you press the buttons in the wrong order, you will get an error or a nonsensical result, so test with a number you know the answer to — like LOG of 100 should always equal 2.

Using secondary functions with Shift or 2nd

If LOG is printed in small text above a key rather than on the key itself, it is a secondary function. Press the Shift key (sometimes labeled "2nd" or "INV") first, then press the key with LOG written above it. The display may show "2nd" or a small indicator light to confirm you are in secondary-function mode.

This is common on calculators where space is limited. For instance, on some models the LOG function shares a key with another operation like multiplication or a trigonometric function. Always check whether the function you want is printed directly on the key or above it before you press.

Understanding what the logarithm result means

When you press LOG and get a result, that number is the exponent you would raise 10 to in order to get your original number. If you enter 1000 and press LOG, you get 3, because 10³ = 1000. If you enter 50 and press LOG, you get approximately 1.699, because 10^1.699 ≈ 50.

Logarithms are used in science, engineering, and finance to work with very large or very small numbers in a more manageable form. They also appear in formulas for sound intensity (decibels), earthquake strength (Richter scale), and chemical acidity (pH). Understanding what the result represents helps you know whether your answer makes sense in context.

Natural logarithm (LN) versus base-10 logarithm (LOG)

The LN button calculates the natural logarithm, which uses the mathematical constant e (approximately 2.718) as its base instead of 10. In most high school math, you will use LOG. In calculus, physics, and higher mathematics, LN appears more often because it has simpler properties for derivatives and integrals.

Both buttons work the same way: enter your number, then press the button. The difference is only in what base is used. If a problem or formula specifies "log" without a base, it usually means base-10 (LOG). If it specifies "ln" or "log base e", use LN. When in doubt, check the problem statement or your textbook.

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

If you have a basic four-function calculator with only addition, subtraction, multiplication, and division, it cannot calculate logarithms. You will need to borrow or purchase a scientific calculator, which costs between $10 and $30 for a basic model.

Many smartphones have a calculator app that switches to scientific mode when you rotate the phone to landscape orientation. This mode includes LOG and LN buttons. Online calculators and spreadsheet programs like Google Sheets (using the LOG10 function) can also compute logarithms if you do not have a physical calculator available.

Common mistakes and how to avoid them

The most frequent error is pressing buttons in the wrong order. Test your calculator with a number you know: LOG of 10 should equal 1, and LOG of 1 should equal 0. If you get different results, you are pressing the buttons in the wrong sequence for your model.

Another mistake is confusing LOG and LN. If your answer seems too large or too small, check whether you used the right button. LOG of 100 is 2; LN of 100 is about 4.6. If your result is drastically different from what you expected, you may have used the wrong function.

Negative numbers and zero also cause problems. You cannot take the logarithm of zero or any negative number — the calculator will display an error. Logarithms are only defined for positive numbers, so if a problem asks you to find LOG of a negative value, something in your setup is wrong.

Frequently Asked Questions

What is the difference between LOG and log₁₀?

They are the same thing. LOG on a calculator is the base-10 logarithm, sometimes written as log₁₀ in textbooks. Both mean "what power do I raise 10 to in order to get this number?"

Why do I get an error when I try to take the logarithm of a negative number?

Logarithms are not defined for negative numbers or zero in regular math. You can only take the logarithm of a positive number. If a problem requires the logarithm of a negative value, you may need to use a different approach or check whether the problem is set up correctly.

Can I use my phone calculator instead of a scientific calculator?

Yes, if your phone's calculator app has a scientific mode. Most smartphones show a scientific calculator when you rotate the phone to landscape or swipe to reveal more functions. Check your app to see whether LOG and LN buttons are available.

If LOG of 100 is 2, why is LOG of 50 not exactly 1.5?

Because logarithms do not scale linearly. LOG of 50 is about 1.699, not 1.5, because the relationship between a number and its logarithm is not a straight line. This is why logarithms are useful — they compress large ranges of numbers into smaller, more manageable ranges.

Do I need to memorize any logarithm values?

No. Your calculator will compute them for you. It is helpful to remember that LOG of 1 is always 0, LOG of 10 is always 1, and LOG of 100 is always 2, because these help you check whether your calculator is working correctly.