How to Put Log in A Calculator
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Reviewed by Calculator Editorial Team
Logarithms are essential in mathematics, science, and engineering. This guide explains how to properly use the log function on a calculator, including the difference between common (base 10) and natural (base e) logarithms.
What is Log in a Calculator?
The log function on a calculator computes logarithms, which are the inverse of exponential functions. There are two main types of logarithms you'll encounter:
- Common logarithm (log₁₀): Uses base 10, commonly used in engineering and science
- Natural logarithm (ln): Uses base e (approximately 2.71828), commonly used in calculus and statistics
Most scientific calculators have dedicated buttons for these functions, typically labeled "log" for common logarithm and "ln" for natural logarithm.
How to Use Log on a Calculator
Using the log function on a calculator is straightforward once you understand the basic steps:
- Enter the number you want to find the logarithm of
- Press the log button (for common logarithm) or ln button (for natural logarithm)
- The calculator will display the result
Note: Make sure your calculator is in the correct mode (usually "DEG" for degrees or "RAD" for radians) before performing logarithmic calculations, as this affects trigonometric functions but not logarithms.
For example, to calculate log₁₀(100):
- Enter 100 on your calculator
- Press the log button
- The result will be 2 (since 10² = 100)
Log Formula
The basic logarithm formula is:
logb(a) = c means bc = a
Where:
- b = base of the logarithm
- a = argument (the number you're taking the log of)
- c = result of the logarithm
For common logarithms (base 10), the formula is:
log₁₀(a) = c means 10c = a
For natural logarithms (base e), the formula is:
ln(a) = c means ec = a
Log Examples
Here are some practical examples of logarithmic calculations:
Example 1: Common Logarithm
Calculate log₁₀(1000):
log₁₀(1000) = 3 because 10³ = 1000
Example 2: Natural Logarithm
Calculate ln(e²):
ln(e²) = 2 because e² = e²
Example 3: Scientific Notation
Calculate log₁₀(1,000,000):
log₁₀(1,000,000) = 6 because 10⁶ = 1,000,000
Log vs. Ln
The main difference between log and ln is the base:
- log typically refers to base 10 logarithms
- ln refers to natural logarithms with base e
You can convert between them using the change of base formula:
logb(a) = ln(a)/ln(b)
For example, to convert log₁₀(100) to natural logarithm:
log₁₀(100) = ln(100)/ln(10) ≈ 2/2.302585 ≈ 0.868589
FAQ
What is the difference between log and ln?
Log typically refers to base 10 logarithms, while ln refers to natural logarithms with base e (approximately 2.71828). The main difference is the base used in the calculation.
How do I calculate logarithms without a calculator?
You can use logarithm tables or the change of base formula to calculate logarithms manually. The change of base formula is logb(a) = ln(a)/ln(b).
What is the domain of the log function?
The domain of the log function is all positive real numbers. In other words, the argument (the number inside the log) must be greater than zero.
Can I use logarithms to solve exponential equations?
Yes, logarithms are often used to solve exponential equations by taking the log of both sides, which allows you to bring the exponent down as a multiplier.