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How to Put Log Into A Calculator

Reviewed by Calculator Editorial Team

Logarithms are essential in mathematics, science, and engineering. This guide explains how to use logarithmic functions in a calculator, including common bases, natural logarithms, and logarithmic identities.

What is Log?

A logarithm (log) is the inverse function of exponentiation. It answers the question: "To what power must a base number be raised to obtain another number?"

There are two main types of logarithms:

  • Common logarithm (base 10): Used in many scientific and engineering applications.
  • Natural logarithm (base e): Used in calculus and advanced mathematics.

Logarithms are widely used in fields like acoustics, chemistry, seismology, and finance to simplify complex calculations.

How to Use Log in a Calculator

Most scientific calculators have a dedicated log button for common logarithms (base 10). For natural logarithms (base e), look for the "ln" button.

Step-by-Step Instructions

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

Common Log Formula: log10(x) = y

Natural Log Formula: ln(x) = y

Log Examples

Let's look at some examples of how to use logarithms in a calculator.

Example 1: Common Logarithm

Find log10(1000):

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

Example 2: Natural Logarithm

Find ln(e2):

  1. Enter e2 (approximately 7.389) on the calculator.
  2. Press the ln button.
  3. The result is 2 because e2 = e2.

Log Formula

The general formula for logarithms is:

logb(a) = c

Where:

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

This formula states that the logarithm of a number a with base b is equal to the exponent c that satisfies bc = a.

Log Calculator

Use the calculator in the sidebar to compute logarithms with different bases. Enter your values and click "Calculate" to see the result.

FAQ

What is the difference between log and ln?
Log typically refers to base 10 logarithms, while ln refers to natural logarithms (base e, approximately 2.71828).
Can I use a calculator to find logarithms of negative numbers?
No, logarithms of negative numbers are not defined in real numbers. The argument must be positive.
What is the logarithm of 1?
The logarithm of 1 with any base is always 0, because any number raised to the power of 0 is 1.