Cal11 calculator
Search calculator...

How to Put Logarithms in A Calculator

Reviewed by Calculator Editorial Team

Logarithms are powerful mathematical tools used in many scientific and engineering fields. This guide explains how to input and calculate logarithms using a standard calculator, including common logarithms (base 10) and natural logarithms (base e).

Basic Logarithms

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

Where:

  • b is the base (must be positive and not equal to 1)
  • a is the argument (must be positive)
  • c is the result (the logarithm)

Most calculators have dedicated logarithm functions for common bases:

  • Common logarithm (base 10): log or lg
  • Natural logarithm (base e): ln

Scientific Notation

Scientific notation is often used with logarithms. A number in scientific notation is written as:

a × 10n

Where:

  • a is a number between 1 and 10
  • n is an integer

For example, 300,000,000 can be written as 3 × 108.

Common Logarithms (Base 10)

Common logarithms use base 10. On most calculators, you'll find this function labeled as "log" or "lg".

How to Calculate Common Logarithms

  1. Enter the number you want to find the logarithm of
  2. Press the "log" or "lg" button
  3. The calculator will display the logarithm (base 10)

Example: log(100) = 2 because 102 = 100.

Common Logarithm Applications

  • pH calculations in chemistry
  • Decibel measurements in acoustics
  • Richter scale measurements in seismology
  • Earthquake magnitude calculations

Natural Logarithms (Base e)

Natural logarithms use base e (approximately 2.71828). On most calculators, this function is labeled as "ln".

How to Calculate Natural Logarithms

  1. Enter the number you want to find the natural logarithm of
  2. Press the "ln" button
  3. The calculator will display the natural logarithm

Example: ln(e) ≈ 1 because e1 ≈ e.

Natural Logarithm Applications

  • Compound interest calculations
  • Growth and decay problems
  • Probability and statistics
  • Calculus and differential equations

Logarithm Properties

Logarithms have several important properties that simplify calculations:

Product Rule

logb(xy) = logb(x) + logb(y)

Quotient Rule

logb(x/y) = logb(x) - logb(y)

Power Rule

logb(xy) = y × logb(x)

Change of Base Formula

logb(x) = logk(x) / logk(b)

Practical Examples

Example 1: Common Logarithm

Calculate log(1000):

  1. Enter 1000 on your calculator
  2. Press the "log" button
  3. The result is 3 because 103 = 1000

Example 2: Natural Logarithm

Calculate ln(√e):

  1. Enter √e on your calculator (this is e1/2)
  2. Press the "ln" button
  3. The result is 0.5 because e0.5 = √e

Example 3: Using Logarithm Properties

Calculate log(200) using the product rule:

  1. Break down 200 into 2 × 100
  2. Calculate log(2) ≈ 0.3010
  3. Calculate log(100) = 2
  4. Add the results: 0.3010 + 2 = 2.3010

FAQ

What is the difference between common and natural logarithms?
Common logarithms use base 10 and are often used in engineering and science. Natural logarithms use base e (approximately 2.71828) and are common in calculus and probability.
Can I calculate logarithms with a basic calculator?
Yes, most scientific calculators have dedicated buttons for common (log) and natural (ln) logarithms. If you only have a basic calculator, you can use the change of base formula.
What happens if I try to calculate the logarithm of a negative number?
Logarithms of negative numbers are not defined in real numbers. The argument of a logarithm must always be positive.
How do I calculate logarithms of numbers less than 1?
For numbers between 0 and 1, the logarithm will be negative. For example, log(0.1) = -1 because 10-1 = 0.1.
Can I use logarithms to solve exponential equations?
Yes, logarithms are often used to solve exponential equations by taking the logarithm of both sides, which converts the equation into a linear form that can be solved for the exponent.