What logarithms do and why your calculator has a button for them

A logarithm is a way of asking: "What power do I raise this number to in order to get that result?" Your calculator's log button answers that question when ready. If you need to know what power you'd raise 10 to in order to get 1,000, the logarithm tells you it's 3 (because 10 to the power of 3 equals 1,000). Without a calculator, this would take trial and error. With one, you press a button.

Most scientific calculators have two logarithm buttons: one labeled LOG (which uses base 10) and one labeled LN (which uses base e, a special number used in science and finance). For everyday use, LOG is what you'll reach for most often. The difference between them matters only if you're working in a specific field — for most people, LOG solves the problem.

You don't need to understand the math deeply to use the button. You need to know what you're trying to find, which button to press, and how to read the answer your calculator gives back.

Key Takeaways

  • The LOG button on your calculator finds what power you need to raise 10 to in order to get your number.
  • To use it, type your number first, then press LOG — the calculator shows the answer when ready.
  • LN is a different logarithm used mainly in science and higher math, not for everyday calculations.
  • Logarithms are useful when you're working with very large numbers, measuring sound or earthquakes, or solving equations where the unknown is in an exponent.

Finding the logarithm of a number on a basic scientific calculator

The steps are straightforward. Type the number you want to find the logarithm of, then press the LOG button. That's it. If you want to know the logarithm of 100, you type 100, press LOG, and the calculator displays 2 (because 10 to the power of 2 is 100).

If your calculator has a two-line display, you'll see your number on the top line and the result on the bottom. If it's a single-line display, the number you typed disappears and the result takes its place. Either way, the answer appears within a second.

On a graphing calculator like a TI-84, the process is identical: type your number, press LOG, read the result. The button is usually in the same spot on every scientific calculator — look for it near other math functions like SIN or square root.

Understanding what the answer means

When you press LOG on the number 1,000, you get 3. This means 10 to the power of 3 equals 1,000. When you press LOG on 10, you get 1 (because 10 to the power of 1 is 10). When you press LOG on 1, you get 0 (because 10 to the power of 0 is 1).

If your number is between 1 and 10, the logarithm will be between 0 and 1 — for example, LOG of 5 is about 0.699. If your number is between 10 and 100, the logarithm will be between 1 and 2. This pattern holds for any number: the logarithm tells you roughly how many digits your number has.

Negative results happen when your number is smaller than 1. LOG of 0.1 is -1 (because 10 to the power of -1 is 0.1). This is normal and correct — it just means you're working with a fraction.

When you'll actually need to use this button

Logarithms appear in real situations more often than you might think. If you're measuring sound in decibels, the scale itself is logarithmic — the LOG button helps you convert between sound pressure and decibels. If you're reading about earthquakes and their magnitude, that scale is also logarithmic. If you're working with pH in chemistry, that's logarithmic too.

In finance, logarithms help calculate compound interest over long periods. In biology, they describe how populations grow or how diseases spread. In any field where you're dealing with numbers that grow very fast or very slow, logarithms are the tool that makes them manageable.

For most people, the most common use is solving an equation where the unknown is in an exponent — for example, "If I invest $1,000 at 5% interest per year, how many years until I have $5,000?" The LOG button gets you there without guessing.

The difference between LOG and LN, and when to use each

LOG uses base 10, which is why it's called the "common logarithm." It's the one you'll use in most everyday situations. LN uses base e (approximately 2.718), which is called the "natural logarithm." It appears in calculus, physics, and higher mathematics, but rarely in practical problems outside those fields.

If you're not sure which one to use, start with LOG. If your textbook or problem says "find the logarithm" without specifying, it means LOG. If it says "find the natural logarithm" or shows "ln" in the problem, use LN instead. The button is usually right next to LOG on your calculator.

Both buttons work the same way: type your number, press the button, read the result. The only difference is which base the calculator uses behind the scenes.

Reversing a logarithm if you need to

Sometimes you know the logarithm and need to find the original number. This is called the "inverse" or "antilog." On most calculators, this is the 10^x button (or sometimes labeled as SHIFT + LOG). If you have the logarithm 2 and want to find what number it came from, you press 2, then press 10^x, and the calculator shows 100.

This is useful when you're working backwards from a result. If a problem tells you "the logarithm of your answer is 3," you use 10^x to find that your answer is 1,000. The inverse of LN is usually labeled e^x and works the same way.

Frequently Asked Questions

What happens if I try to find the logarithm of a negative number?

Your calculator will display an error, usually "ERR" or "DOMAIN ERROR." Logarithms of negative numbers don't exist in regular math — this is a built-in limit, not a calculator mistake. If you're getting this error, check that you typed your number correctly.

Can I use the LOG button on my phone's calculator?

Most phone calculators don't show the LOG button in standard view. On iPhone, rotate your phone to landscape mode and the scientific calculator appears with LOG and LN buttons. On Android, open your calculator app and look for a menu or "scientific" mode that reveals the advanced buttons.

Why do I get a decimal instead of a whole number?

Because most numbers aren't perfect powers of 10. LOG of 50 is about 1.699, not a whole number — that's correct. The decimal tells you exactly where 50 falls between 10 (which has a logarithm of 1) and 100 (which has a logarithm of 2). Your calculator is working properly.

Do I need to memorize logarithm values?

No. The whole point of the LOG button is that you don't have to. Press the button and the calculator does the work. You only need to remember which button to press and what the result means.