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How to Put in Logarithms on A Calculator

Reviewed by Calculator Editorial Team

Logarithms are essential in mathematics, science, and engineering. This guide explains how to input logarithms on a calculator, including common logarithm (log), natural logarithm (ln), and scientific notation.

Basic Logarithm Calculation

A logarithm answers the question: "To what power must a base number be raised to obtain another number?" The general form is:

logb(a) = c means bc = a

For example, log2(8) = 3 because 23 = 8.

Step-by-Step Calculator Input

  1. Turn on your calculator and ensure it's in the appropriate mode (usually "LOG" or "MATH").
  2. Enter the base number (b) first.
  3. Press the logarithm function button (often labeled "log" or "LOG").
  4. Enter the argument number (a).
  5. Press the equals (=) button to get the result (c).

Most scientific calculators have a dedicated "log" button for common logarithms (base 10) and a "ln" button for natural logarithms (base e ≈ 2.71828).

Using Scientific Notation

Scientific notation is useful for very large or very small numbers. It's often required when calculating logarithms.

Scientific notation: a × 10n where 1 ≤ a < 10 and n is an integer

Example: 300,000 = 3 × 105

Inputting in Scientific Notation

  1. Enter the coefficient (a).
  2. Press the exponent button (often labeled "EE" or "EXP").
  3. Enter the exponent (n).
  4. Continue with the logarithm calculation.

Natural Logarithm (ln)

The natural logarithm uses base e (approximately 2.71828). It's commonly used in calculus and exponential growth/decay problems.

ln(a) = c means ec = a

Example: ln(7.389) ≈ 2 because e2 ≈ 7.389.

Calculator Input

  1. Ensure your calculator is in the natural logarithm mode (often labeled "ln").
  2. Enter the argument number (a).
  3. Press the equals (=) button to get the result (c).

Common Logarithm (log)

The common logarithm uses base 10. It's widely used in fields like pH calculations and decibel measurements.

log(a) = c means 10c = a

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

Calculator Input

  1. Ensure your calculator is in the common logarithm mode (often labeled "log").
  2. Enter the argument number (a).
  3. Press the equals (=) button to get the result (c).

Logarithm Properties

Understanding these properties helps simplify logarithm calculations:

Property Formula Example
Product Rule logb(xy) = logb(x) + logb(y) log(20) = log(2) + log(10)
Quotient Rule logb(x/y) = logb(x) - logb(y) log(5) = log(10) - log(2)
Power Rule logb(xy) = y × logb(x) log(64) = 2 × log(8)

These properties can be used to simplify complex logarithm calculations before inputting them on a calculator.

Common Mistakes

Avoid these errors when calculating logarithms:

  • Using the wrong logarithm function (common vs. natural)
  • Forgetting to use scientific notation for very large or small numbers
  • Incorrectly entering the base number (if not using standard functions)
  • Not checking the calculator mode before calculation

Always verify your calculator is in the correct mode before performing logarithm calculations.

Frequently Asked Questions

What's the difference between log and ln?

The "log" function typically refers to the common logarithm (base 10), while "ln" refers to the natural logarithm (base e ≈ 2.71828).

How do I calculate logarithms of negative numbers?

Logarithms of negative numbers are not defined in real numbers. They can be calculated in complex numbers, but this is beyond basic calculator usage.

What if my calculator doesn't have a logarithm function?

You can use the natural logarithm (ln) function and convert it to common logarithm using the formula: log10(x) = ln(x)/ln(10).