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How to Put Log on Calculator

Reviewed by Calculator Editorial Team

Logarithms are essential in mathematics, science, and engineering. This guide explains how to use logarithms on a calculator, including common and natural logarithms, with practical examples and step-by-step instructions.

How to Use Log on a Calculator

Using logarithms on a calculator is straightforward once you understand the basic concepts. Most scientific calculators have dedicated logarithm functions, typically labeled as "log" for common logarithms (base 10) and "ln" for natural logarithms (base e).

Logarithm Formula

logb(x) = y means by = x

Step-by-Step Instructions

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

Tip

Always check which logarithm function your calculator uses. Some calculators may have different labels for the same function.

Logarithm Basics

Logarithms are the inverse functions of exponential functions. They help solve equations with variables in the exponent. The logarithm of a number is the exponent to which another fixed number, called the base, must be raised to produce the original number.

Term Definition
Logarithm The exponent to which a base must be raised to obtain a given number.
Base The fixed number used in the logarithm calculation.
Argument The number for which the logarithm is calculated.

Common Logarithm (Base 10)

The common logarithm, denoted as log(x), uses base 10. It's widely used in fields like pH calculations, decibel measurements, and engineering applications.

Common Logarithm Formula

log10(x) = y means 10y = x

Example Calculation

Find log10(1000):

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

Natural Logarithm (Base e)

The natural logarithm, denoted as ln(x), uses base e (approximately 2.71828). It's commonly used in calculus, statistics, and physics.

Natural Logarithm Formula

ln(x) = y means ey = x

Example Calculation

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.

Logarithm Examples

Here are some practical examples of logarithms in different contexts:

Context Example Calculation
pH Calculation Find the pH of a solution with [H+] = 1 × 10-5 M pH = -log10(1 × 10-5) = 5
Sound Level Calculate the sound level in decibels for a sound with intensity 10-12 W/m2 L = 10 × log10(10-12/10-16) = 40 dB
Compound Interest Find the time required for $1000 to grow to $2000 at 5% annual interest compounded continuously t = (ln(2) - ln(1))/0.05 ≈ 13.86 years

FAQ

What is the difference between log and ln?

The main difference is the base used. "log" typically refers to base 10 (common logarithm), while "ln" refers to base e (natural logarithm).

How do I calculate logarithms without a calculator?

You can use logarithm tables or properties of logarithms to simplify calculations. For example, log(ab) = log(a) + log(b).

What are the common applications of logarithms?

Logarithms are used in pH calculations, sound level measurements, compound interest calculations, earthquake magnitude scales, and more.

Can I use logarithms to solve exponential equations?

Yes, logarithms can help solve equations where the variable is in the exponent by taking the logarithm of both sides.