What the log button does

The log button on a scientific 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 to the power of 2 equals 100. Most scientific calculators use "log" to mean base-10 logarithm, which is the standard in science and engineering.

When you press the log button, you are not doing anything mysterious — you are asking the calculator to solve an exponent problem backwards. Instead of asking "what is 10 to the 3rd power?" you are asking "10 to what power gives me 1000?" The answer is 3.

Some calculators also have an ln button, which calculates the natural logarithm (base e, approximately 2.718). The process is identical — you enter a number and press the button. Which one you use depends on what you are calculating. Most everyday math and science uses log (base 10), while higher math and some sciences use ln (natural log).

Key Takeaways

  • Press the number first, then the log button — the order matters and varies by calculator model.
  • The log button finds what power of 10 produces your number, so log(1000) = 3 because 10³ = 1000.
  • Scientific calculators show the result on the display when ready after you press log.
  • The ln button works the same way but uses base e instead of base 10, and is used in different types of math.

The order of button presses on different calculator types

Most modern scientific calculators use postfix notation: you enter the number first, then press log. For example, to find log(50), you type 5, 0, then press the log button. The answer appears on the display.

Some older or specialized calculators use prefix notation, where you press log first, then enter the number. These are less common in schools and offices today, but if your calculator has this layout, you would press log, then 5, 0, then equals. Check your calculator's manual or try both ways with a number you know — log(100) should always equal 2.

Graphing calculators and scientific calculators built into computers often show the function name in parentheses on screen: log(). In these cases, you type the number inside the parentheses, then press enter. The display will show something like "log(50)" before you press enter, then the result after.

Working with negative results and numbers less than 1

Logarithms of numbers between 0 and 1 produce negative results. For example, log(0.1) = -1, because 10 to the power of -1 equals 0.1. This is correct — your calculator is not broken. The negative sign tells you that the number is smaller than 1.

You cannot take the logarithm of zero or any negative number on a standard calculator. If you try, the display will show an error like "ERR" or "undefined". This is because there is no power of 10 that produces zero or a negative number — logarithms only work on positive numbers.

If you are working with a negative number and need its logarithm, take the logarithm of the absolute value (the number without the minus sign), then note that the original number was negative. For example, to work with log(-50), you would calculate log(50) ≈ 1.699, but remember the input was negative.

Practical examples you can test right now

Try these on your calculator to see how log works. Enter 1000 and press log — you should get 3. Enter 10 and press log — you should get 1. Enter 1 and press log — you should get 0. These three examples show the pattern: log(10ⁿ) always equals n.

Now try a number that is not a power of 10. Enter 50 and press log. You should get approximately 1.699. This means 10 to the power of 1.699 equals 50. You can verify this makes sense: 10¹ = 10 and 10² = 100, so 50 falls between them, and 1.699 is between 1 and 2.

Try entering 0.01 and pressing log. You should get -2, because 10 to the power of -2 equals 0.01. This shows how negative logarithms work: they represent numbers smaller than 1.

When you need ln instead of log

The ln button calculates the natural logarithm, which uses the number e (approximately 2.718) instead of 10. In most high school math and general science, you use log. In calculus, statistics, physics, chemistry, and biology, you often use ln.

The process is identical: enter your number, press ln, and read the result. For example, ln(10) ≈ 2.303, while log(10) = 1. Both are correct — they just answer different questions. Log asks "10 to what power?" while ln asks "e to what power?"

If you are following a textbook or assignment and it says "find the logarithm" without specifying which one, check the context. If the problem mentions e, exponential growth, or calculus, use ln. If it is general math or science, use log. When in doubt, ask your instructor or check the problem's earlier examples.

Fixing common mistakes

The most common error is pressing the buttons in the wrong order. If your calculator shows an error or a nonsensical result, try reversing the order. If you pressed log first and got an error, try entering the number first instead.

Another mistake is forgetting that log only works on positive numbers. If you get an error and you entered a negative number or zero, that is why. Rethink your problem — you may need to take the log of the absolute value, or your calculation may have gone wrong earlier.

If your result seems too large or too small, double-check that you entered the number correctly. Entering 50 instead of 500 will give you log(50) ≈ 1.699 instead of log(500) ≈ 2.699. A small typing error creates a noticeably different answer.

Frequently Asked Questions

What is the difference between log and ln?

Log uses base 10 (the standard in science and engineering), while ln uses base e, a special number approximately equal to 2.718 (used in calculus and advanced math). Both buttons work the same way — enter a number and press the button — but they answer different questions about exponents.

Why do I get a negative number when I press log?

A negative logarithm is correct when your number is between 0 and 1. For example, log(0.1) = -1 because 10 to the power of -1 equals 0.1. The negative sign is part of the answer, not an error.

Can I find the log of a negative number?

No. Standard calculators cannot find the logarithm of a negative number or zero. Logarithms only work on positive numbers. If you need to work with a negative number, take the log of its absolute value (the number without the minus sign).

My calculator shows "log(" on the screen — what do I do?

Your calculator is waiting for you to type the number. Type the number inside the parentheses, then press enter or equals. For example, type 50, then press enter, and the calculator will show the result of log(50).

How do I know if I should use log or ln?

Check your textbook or assignment. If it mentions e, exponential functions, or calculus, use ln. If it is general math, science, or engineering, use log. When the problem does not specify, log (base 10) is the safer choice for most everyday calculations.