how to put logs in calculator

If you have ever wondered how to type logs into a calculator, you are not alone. Many students know the formula on paper but get stuck the moment they see buttons labeled log, ln, or LOGBASE. This guide will show you exactly what to press and why.

What does “log” mean on a calculator?

A logarithm asks: “What exponent gives me this number?”

• log(x) usually means base 10.
• ln(x) means base e (about 2.71828).
• log_b(x) means logarithm with custom base b.

Example: log(1000) = 3, because 10³ = 1000.

Where to find log buttons

Scientific calculators

Most scientific calculators have dedicated keys:

• log for base 10
• ln for natural log

Some models also support custom base directly through a shifted function.

Phone calculator apps

On many phones, rotate to landscape mode to reveal scientific functions. You should then see log and ln buttons.

Graphing calculators (TI/Casio, etc.)

Graphing calculators often include:

• Direct log( and ln( functions
• A menu function for logBASE( or equivalent

How to put logs in your calculator (step-by-step)

1) Common log: log(x)

• Press log
• Type the number (x)
• Close parenthesis if needed
• Press =

Example: log(100) = 2.

2) Natural log: ln(x)

• Press ln
• Type the number (x)
• Press =

Example: ln(e) = 1.

3) Custom base log: log_b(x)

If your calculator does not have a direct log-base button, use change-of-base:

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

• Type log(x)
• Divide by log(b)
• Press =

Example: log₂(8) = log(8) / log(2) = 3.

Common mistakes and fixes

• Using zero or negative x: logs require x > 0.
• Using invalid base: base must be > 0 and not equal to 1.
• Mixing log and ln: be sure your class expects base 10 or base e.
• Missing parentheses: especially on graphing calculators.

Quick practice examples

Example A

Find log(10000). Since 10⁴ = 10000, answer is 4.

Example B

Find ln(1). Since e⁰ = 1, answer is 0.

Example C

Find log₅(125). Since 5³ = 125, answer is 3. If needed, compute log(125)/log(5).

Final tip

If you are unsure, test your result by converting back to exponential form. For example, if you got log₃(81) = 4, check whether 3⁴ = 81. If yes, your log entry was correct.