What the Log Button Does
The log button on your calculator finds the logarithm of a number. A logarithm answers the question: "What power do I raise 10 to in order to get this number?" For example, log(100) = 2, because 10 raised to the power of 2 equals 100. Most scientific calculators have a dedicated log button that assumes base 10 unless you tell it otherwise.
You will see the log button labeled as LOG or sometimes log₁₀. It is different from the LN button, which calculates natural logarithm (base e, used in science and engineering). If you press log by mistake when you need LN, or vice versa, your answer will be wrong, so knowing which one you need before you start matters.
Key Takeaways
- The log button finds what power you raise 10 to in order to get your number — log(1000) = 3 because 10³ = 1000.
- Enter the number first, then press log; most calculators show the result when ready without requiring you to press equals.
- Log of 1 always equals 0, and log of any number less than 1 gives a negative result.
- If your calculator has a second function menu, you may need to press Shift or 2nd before log to access it on some models.
The Basic Steps to Use Log
The process is straightforward on most scientific calculators. First, turn on your calculator and make sure it is in standard mode (not programming mode or statistical mode). Then type the number you want to find the logarithm of — for example, 50.
Next, press the LOG button. On most calculators, the result appears when ready on the display. You do not need to press the equals button. If nothing happens, check whether your calculator requires you to press Shift or 2nd first to access the log function — some models hide it behind a second function menu.
For the number 50, the log will show approximately 1.699. This means 10 raised to the power of 1.699 equals 50. You can verify this on the same calculator by pressing 10, then the power button (usually ^ or x^y), then 1.699, then equals.
Where the Log Button Is Located
On a standard scientific calculator, the log button sits in the upper rows, usually grouped with other math functions like sin, cos, and tan. It is almost never on the main number pad. Look for it near the trigonometry buttons or near the natural logarithm (LN) button — they are usually close together.
On graphing calculators like the TI-84, the log button is in the math menu. Press the MATH button, scroll to find LOG, and select it. The calculator will then prompt you to enter the number. On phone calculator apps, log may be hidden — swipe or rotate your phone to landscape mode to reveal the scientific calculator view, where log appears alongside other advanced functions.
Common Results and What They Mean
Log of 1 always equals 0, no matter what calculator you use. This is because 10 to the power of 0 equals 1. Log of 10 always equals 1, because 10 to the power of 1 is 10. Log of 100 equals 2, log of 1000 equals 3, and so on — each time you multiply by 10, the log increases by 1.
If you enter a number smaller than 1 — say, 0.5 — the log will be negative, around −0.301. This is correct. Negative logarithms are common and not an error. If you enter 0 or a negative number, the calculator will show an error or "undefined" because logarithms of zero and negative numbers do not exist in standard mathematics.
Log Versus LN: Which One to Use
The LOG button uses base 10. The LN button uses base e (approximately 2.718), called the natural logarithm. Your textbook or problem will tell you which one you need. If it says "log" without specifying, it almost always means base 10 log. If it says "ln" or "natural log", use the LN button instead.
Using the wrong one is a common mistake. Log(100) = 2, but LN(100) ≈ 4.605. The numbers are very different, so if your answer seems way off, double-check that you pressed the right button. Some calculators let you change the base using a menu option, but the default log button is always base 10.
Troubleshooting When Log Does Not Work
If you press log and nothing happens, the most likely cause is that your calculator is in the wrong mode or the function is hidden. Check whether you need to press Shift, 2nd, or Function first. Some calculators require you to press this modifier key before accessing secondary functions. Try pressing it, then log, then your number.
If you see an error message after pressing log, you probably entered a number that logarithms cannot handle — either 0, a negative number, or you may have typed something by accident. Clear the display and try again with a positive number greater than 0. If the calculator still will not respond, check the manual or look up your specific model online, as some older or specialized calculators have different button layouts.
Frequently Asked Questions
What is the difference between log and log base 2?
The log button on your calculator is base 10. Log base 2 is different — it answers "what power do I raise 2 to?" Most calculators do not have a dedicated base 2 button. If you need log base 2, you can use the change of base formula: log₂(x) = log(x) ÷ log(2). Enter your number, press log, then divide by log(2).
Can I use log on a basic four-function calculator?
No. Basic calculators that only add, subtract, multiply, and divide do not have a log function. You need a scientific calculator, which costs between $10 and $30 and is available at any office supply store or online. Most phones also have a scientific calculator app built in.
Why does log of a decimal number give a negative answer?
Because 10 raised to a negative power gives a decimal. For example, 10 to the power of −1 equals 0.1, so log(0.1) = −1. This is correct behavior, not an error. Negative logarithms are used in science and engineering all the time.
Do I need to press equals after pressing log?
On most modern scientific calculators, no — the result appears as soon as you press log. On some older models or graphing calculators, you may need to press equals. If you are unsure, try it both ways. Pressing equals when it is not needed usually does not hurt.
What if my calculator shows "Math Error" when I press log?
You entered a number that logarithms cannot process — either 0, a negative number, or the calculator did not register your input correctly. Clear the display, enter a positive number like 10 or 100, and try again. If it still fails, your calculator may need new batteries or there may be a hardware problem.