how to do log on calculator

What does “log” mean on a calculator?

On most scientific calculators, the LOG button means base-10 logarithm, written as log(x) or log10(x). The LN button means natural logarithm, written as ln(x), which is log base e (about 2.71828).

In plain language, a logarithm answers this question: “What power do I raise the base to, to get this number?”

• log(1000) = 3 because 103 = 1000
• ln(e4) = 4 because e4 = e4

Quick answer: which button should I press?

If the problem says log(x)

Press LOG, enter the number, then press =.

If the problem says ln(x)

Press LN, enter the number, then press =.

If the problem says log with another base, like log₂(40)

Some calculators have a direct logBASE function. If yours does not, use change of base: logb(x) = ln(x)/ln(b) (or log(x)/log(b)).

Step-by-step: how to do log on a scientific calculator

1) Check the expression

Identify whether it is common log (log), natural log (ln), or another base (logb).

2) Enter parentheses when needed

For clean input, many calculators accept log(250) style. If your calculator supports immediate entry, pressing LOG first then typing the number also works.

3) Use change-of-base for custom bases

For example, to compute log2(40):

1. Compute ln(40)
2. Compute ln(2)
3. Divide: ln(40) ÷ ln(2)

Result is about 5.3219.

Worked examples

Example 1: log(1000)

Press LOG then 1000. You should get 3.

Example 2: ln(7)

Press LN then 7. Result is about 1.9459.

Example 3: log₃(50)

Use change-of-base: log3(50) = ln(50) / ln(3) ≈ 3.5609.

Important rules and restrictions

• The number inside a log must be positive (x > 0).
• For logb(x), base must satisfy b > 0 and b ≠ 1.
• log(1) = 0 for any valid base.
• logb(b) = 1.

Common mistakes students make

• Using LOG when the question asks for LN.
• Trying to compute log of zero or a negative number.
• Forgetting parentheses in longer expressions.
• Typing ln(x)/ln(b) incorrectly as ln(x/ln(b)).
• Rounding too early, which can cause errors in multi-step problems.

How to check your answer

If you computed logb(x) = y, verify by raising the base: by. If your result is close to x, your log is likely correct.

Final tip

The fastest way to avoid mistakes is to memorize this trio:

• LOG = base 10
• LN = base e
• Any base = change-of-base formula

Bookmark this page and use the calculator above whenever you need a quick, reliable logarithm result.