how to use logarithm on calculator

If you've ever stared at a calculator and wondered what the log and ln buttons actually do, you're not alone. Logarithms are a shortcut for solving exponent questions. Instead of asking “What is 10 raised to this power?”, logs ask: “What power do I need to get this number?”

This guide walks you through how to use logarithms on a calculator step by step, even if you're just getting started.

What is a logarithm?

A logarithm answers this question:

base^answer = number

For example:

• log₁₀(100) = 2, because 10² = 100
• log₂(8) = 3, because 2³ = 8
• ln(e) = 1, because e¹ = e

Know your calculator buttons: LOG vs LN

LOG button

On most scientific calculators, LOG means base-10 logarithm: log₁₀(x).

LN button

LN means natural log, base e (approximately 2.71828): ln(x).

How to do log base 10 on a calculator

1. Turn on your scientific calculator.
2. Enter the number (for example, 1000).
3. Press the LOG button (or LOG first, then number depending on model).
4. Read the result.

Example: log₁₀(1000) = 3.

How to do natural log (ln) on a calculator

1. Enter a positive number, such as 7.5.
2. Press LN.
3. Your calculator gives the natural log value.

Example: ln(7.5) ≈ 2.0149.

How to calculate logarithm with any base (like log₂ or log₅)

Some calculators have a dedicated log base feature, but many do not. If your calculator doesn't, use the change of base formula:

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

or equivalently:

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

Example: Find log₂(64)

• Compute log(64)
• Compute log(2)
• Divide: log(64) ÷ log(2) = 6

So log₂(64) = 6.

Using the calculator above on this page

• Select Common logarithm for log₁₀(x).
• Select Natural logarithm for ln(x).
• Select Custom base to compute log_b(x).
• For custom base, provide both x and b.

The tool checks invalid inputs and shows a clear result with the expression used.

Common mistakes (and how to fix them)

1) Trying to log a negative number

For real-number math, logarithms are only defined for x > 0. If x is 0 or negative, you'll get an error.

2) Using base 1

Base 1 is invalid for logarithms. A valid base must be b > 0 and b ≠ 1.

3) Mixing up LOG and LN

If your homework asks for natural log but you use LOG, your answer will be wrong. Always check the required base.

4) Parentheses issues

On some calculators, you'll need to type expressions like log(64) ÷ log(2) with proper parentheses to avoid order-of-operation mistakes.

Where logarithms are used in real life

• Finance: compound growth models
• Science: pH, earthquake magnitude, sound intensity
• Computer science: algorithm complexity and data structures
• Statistics: log transformations to normalize data

Practice questions

1. log₁₀(10,000) = ?
2. ln(1) = ?
3. log₃(81) = ?

Answers: 4, 0, and 4.

Final takeaway

To use logarithms on a calculator confidently:

• Use LOG for base 10.
• Use LN for base e.
• Use change of base for any other base.

Once you practice a few examples, log calculations become quick and routine.