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How to Put Log Into The Calculator

Reviewed by Calculator Editorial Team

Logarithms are essential mathematical functions used in calculators for solving exponential equations, analyzing growth rates, and simplifying complex calculations. This guide explains how to properly input and use logarithmic functions in calculators, including common bases (base 10 and natural logarithm), syntax, and practical applications.

What is Log in Calculators?

The term "log" in calculators refers to logarithmic functions, which are the inverse of exponential functions. There are two main types of logarithms used in calculators:

  • Common logarithm (base 10): Denoted as log₁₀(x) or simply log(x) in many calculators
  • Natural logarithm (base e): Denoted as ln(x) where e ≈ 2.71828
logₐ(b) = c means aᶜ = b

Logarithms help solve equations where the variable is in the exponent, such as solving for x in 2ˣ = 8. The solution is x = log₂(8) = 3.

How to Use Log Functions

Step 1: Select the Log Function

Most scientific calculators have a "log" button for common logarithms and an "ln" button for natural logarithms. Some calculators may require you to press the "shift" or "2nd function" button first.

Step 2: Enter the Number

After selecting the log function, enter the number you want to find the logarithm of. For example, to calculate log(100), press the "log" button followed by "1", "0", "0".

Step 3: Calculate

Press the equals (=) button to get the result. For log(100), the calculator will display 2 because 10² = 100.

Note: Some calculators may require you to enter the base first. If your calculator has a "log" function that requires a base, you may need to enter the base first, then the number.

Common Uses of Logarithms

Logarithms are used in various scientific and mathematical applications:

  1. Solving exponential equations: Find x in equations like 3ˣ = 27
  2. Measuring earthquake intensity: Richter scale uses base 10 logarithms
  3. Analyzing pH levels: pH = -log[H⁺] concentration
  4. Calculating sound intensity: Decibels use logarithmic scale
  5. Financial calculations: Compound interest and growth rates

Practical Examples

Example 1: Common Logarithm

Calculate log(1000):

  1. Press "log" button
  2. Enter "1", "0", "0", "0"
  3. Press "="
  4. Result: 3 (since 10³ = 1000)

Example 2: Natural Logarithm

Calculate ln(e²):

  1. Press "ln" button
  2. Enter "e" (if available) or "2.71828" twice
  3. Press "="
  4. Result: 2 (since e² = e²)

Example 3: Solving an Equation

Solve 5ˣ = 125:

  1. Press "log" button
  2. Enter "1", "2", "5"
  3. Press "÷" (division)
  4. Press "log" button
  5. Enter "5"
  6. Press "="
  7. Result: 3 (since 5³ = 125)

FAQ

What is the difference between log and ln?
Log refers to base 10 logarithms, while ln refers to natural logarithms with base e (approximately 2.71828).
How do I calculate logarithms with different bases?
Use the change of base formula: logₐ(b) = logₖ(b)/logₖ(a) where k is any positive number. Most calculators have a built-in log function for base 10.
What happens if I try to calculate log(0)?
Log(0) is undefined in real numbers because there's no power of any positive number that equals zero.
Can I use logarithms to solve any exponential equation?
Yes, logarithms can solve any exponential equation where the variable is in the exponent, provided the base is positive and not equal to 1.