how to do logarithms on calculator

If you have ever stared at the log and ln keys on a scientific calculator and wondered what to press, you are not alone. Logarithms feel abstract at first, but calculator steps are actually straightforward once you know what each key means.

This guide will show you exactly how to do logarithms on a calculator, including common log, natural log, and logarithms with any base. It also covers common mistakes and quick ways to check your answer.

Quick answer: which key should you use?

• Use LOG for base 10 logarithms, written as log(x) or log₁₀(x).
• Use LN for natural logarithms (base e), written as ln(x).
• For other bases like log₂(8) or log₅(125), use the change-of-base formula if your calculator does not have a dedicated log-base template.

Step-by-step: how to do each type of logarithm

1) Common logarithm: log₁₀(x)

Suppose you need log(1000).

1. Type 1000 (or press LOG first on some calculators).
2. Press LOG.
3. Press = if needed.

You should get 3, because 10³ = 1000.

2) Natural logarithm: ln(x)

Suppose you need ln(20).

1. Enter 20.
2. Press LN.
3. Press = if your model requires it.

The answer is approximately 2.9957.

3) Any base logarithm: log_b(x)

If your calculator does not have a direct logBASE key, use:

log_b(x) = log(x) / log(b)  or  log_b(x) = ln(x) / ln(b)

Example: find log₂(40).

1. Calculate log(40).
2. Calculate log(2).
3. Divide the first result by the second.

Result: approximately 5.3219.

If your calculator has a log base template

Many modern scientific calculators (especially graphing models) include a built-in template like log(□,□) or logBASE. In that case:

• Put the base in the base slot.
• Put the argument (the number) in the argument slot.
• Evaluate directly.

For instance, log₃(81) gives 4 because 3⁴ = 81.

Doing inverse logarithms (antilogs)

Sometimes you are given the log value and need the original number.

• Inverse of log(x) is 10^x (often SHIFT + LOG).
• Inverse of ln(x) is e^x (often SHIFT + LN).

Example: if log(x) = 2.4, then x = 10^2.4 ≈ 251.19.

Common mistakes students make

• Using the wrong key: pressing LN when the problem asks for base 10 LOG.
• Forgetting parentheses: especially in expressions like log(3x + 1).
• Trying to log a negative number or zero: this causes math error.
• Mixing up base and argument: in log_b(x), b is base, x is number.
• Rounding too early: keep more digits until the final step.

How to check your answer quickly

Use exponent form. If you compute log_b(x)=y, then check whether b^y ≈ x.

Example: if log₂(40) ≈ 5.3219, then calculate 2^5.3219. You should get very close to 40.

Practice set (with answers)

1. log(100) → 2
2. ln(1) → 0
3. log₂(32) → 5
4. log₄(64) → 3
5. ln(10) → 2.3026 (approx)

Final takeaway

To do logarithms on a calculator confidently, remember this simple map: LOG = base 10, LN = base e, and for other bases use change of base. With those three tools, you can solve nearly every log question you'll see in algebra, precalculus, statistics, chemistry, and finance.