What the log button does
The log button on your calculator finds the power you need to raise 10 to in order to get your number. If you press log 100, the calculator returns 2, because 10 to the power of 2 equals 100. If you press log 1000, it returns 3. It is a way to work backwards from an answer to the exponent.
Most scientific calculators have two logarithm buttons: log (which means log base 10) and ln (which means natural log, or log base e). The log button is the one you will use most often in everyday math. The ln button is used in higher mathematics and science, but works the same way — it just uses a different base number.
Logarithms are useful when you are working with very large or very small numbers, or when you need to solve for an unknown exponent. They also show up in real-world problems like calculating how long it takes money to grow, how loud a sound is, or how much of a radioactive material remains after time passes.
Key Takeaways
- The log button finds the exponent: log 100 = 2 because 10² = 100.
- You enter the number first, then press log; the calculator shows the result on the next line.
- Log only works on positive numbers — you cannot take the log of zero or a negative number.
- The ln button works the same way but uses a different base (e instead of 10), and is used in science and higher math.
- If your calculator shows an error when you press log, check that you entered a positive number greater than zero.
Step-by-step: finding a logarithm
Start with a number you want to find the log of. Let's say you want to know log 50. Turn on your calculator and make sure it is in standard mode (not programming mode). Type 50 into the display.
Now press the log button. On most calculators, this button is clearly labeled "log" and is usually in the upper rows near other math functions. The calculator will compute the answer and show it on the display — in this case, about 1.699. That means 10 to the power of 1.699 equals 50.
If your calculator has a two-line display, you will see your original number on the top line and the result on the bottom. If it has a single-line display, the original number disappears and only the result shows. Either way, the answer is the same.
Understanding what the answer means
When you press log 50 and get 1.699, that number tells you the exponent. If you took 10 and raised it to the power of 1.699, you would get 50. You can check this on your calculator: press 10, then the exponent button (usually labeled ^ or x^y), then 1.699, then equals. You should get back to 50 (or very close, depending on rounding).
The answer will always be a decimal when you are taking the log of a number that is not a power of 10. Log 10 = 1 (because 10¹ = 10). Log 100 = 2 (because 10² = 100). Log 1000 = 3. But log 50 falls between 10¹ and 10², so the answer is between 1 and 2.
Numbers smaller than 1 will give you a negative log. For example, log 0.1 = -1, because 10 to the power of -1 equals 0.1. This is correct and expected — it does not mean you made a mistake.
When you cannot take a logarithm
The log button will not work on zero or on negative numbers. If you try to press log 0 or log -5, your calculator will show an error message (often "E" or "Error" or "Math Error"). This is not a broken calculator — logarithms of zero and negative numbers do not exist in regular math.
If you are working on a problem and you need the log of a negative number, it usually means you made an error earlier in your work. Go back and check your setup. If the problem itself asks for the log of a negative number, that is a sign the problem is not solvable using standard logarithms.
Log versus ln: which one to use
Use the log button (base 10) for most everyday problems, especially in science classes, engineering, and when you are working with measurements like pH, sound levels (decibels), or earthquake magnitude. These real-world scales are built on base-10 logarithms.
Use the ln button (natural log, base e) when you are solving problems about growth and decay — like compound interest, population growth, radioactive decay, or cooling. You will also use ln in calculus and higher mathematics. The button works exactly the same way: type your number, press ln, and read the result.
If you are not sure which one a problem is asking for, read the problem statement carefully. It will usually say "log" or "ln" or "log base 10" or "natural log". If it just says "log" without specifying, it almost always means base 10.
Solving for an unknown exponent
One of the most useful things logarithms do is let you solve for an unknown exponent. Suppose you know that 10 to some power equals 500, but you do not know what that power is. You can use the log button to find it.
Press log 500 on your calculator. You get about 2.699. That means 10^2.699 = 500. You have just solved for the exponent without guessing or trial and error. This is how logarithms are used in real problems: you know the result, you know the base, and you need to find the exponent.
Common mistakes and how to fix them
The most common mistake is pressing the number and the log button in the wrong order. Always type the number first, then press log. If you press log first and then type the number, your calculator will not work the way you expect (and some calculators will give you an error).
Another mistake is forgetting that log only works on positive numbers. If you get an error, check that your number is greater than zero. A third mistake is confusing log and ln. If your answer seems way too big or too small, check that you used the right button for the problem you are solving.
Finally, remember that the log button gives you a decimal answer most of the time. Do not round too early in your work — keep the full decimal on your calculator display and only round at the very end when you write down your final answer. Rounding early can make your final answer less accurate.
Frequently Asked Questions
What does it mean if the log is negative?
A negative log is correct and normal. It means your original number is smaller than 1. For example, log 0.01 = -2, because 10 to the power of -2 equals 0.01. Negative logs show up in real problems like pH (which measures acidity) and sound levels.
Can I use log on a phone calculator?
Yes. On most phones, open the calculator app and rotate your phone to landscape mode. The scientific calculator view will appear, and you will see the log and ln buttons. The steps are the same: type your number, then press log.
Why do I get a decimal instead of a whole number?
Most numbers do not have whole-number logarithms. Only powers of 10 do: log 10 = 1, log 100 = 2, log 1000 = 3. Every other positive number gives a decimal. That decimal is the exact answer — you do not need to round it unless the problem asks you to.
What is the difference between log and log base 10?
They are the same thing. When someone writes "log" without a base number, they mean log base 10. The log button on your calculator is log base 10. Some textbooks write it as "log₁₀" to be extra clear, but it is the same button.
Can I undo a logarithm?
Yes. If you have a log answer and want to find the original number, use the 10^x button (sometimes labeled as the inverse of log, or as a second function). Type your log answer, press 10^x, and you get back the original number. This is called taking the antilog or the inverse log.