1. What is Logarithm Base 3?

The logarithm base 3 of a number is the exponent to which 3 must be raised to produce that number. For example, log₃(9) = 2 because 3² = 9.

2. How Does the Calculator Work?

The calculator uses the logarithmic formula:

Where:

• \( x \) — The input number (must be positive)
• \( \ln \) — Natural logarithm (base e)

Explanation: The calculator converts the log base 3 problem into a ratio of natural logarithms which can be easily computed.

3. Importance of Logarithm Calculations

Details: Logarithms are fundamental in mathematics and science, used in algorithms, decibel scales, pH calculations, and more. Base 3 logarithms are particularly useful in computer science (ternary systems) and certain growth calculations.

4. Using the Calculator

Tips: Enter any positive number to calculate its logarithm base 3. The default value is 9 which demonstrates the classic example log₃(9) = 2.

5. Frequently Asked Questions (FAQ)

Q1: Why does log₃(9) equal 2?
A: Because 3 raised to the power of 2 (3²) equals 9.

Q2: What is the value of log₃(1)?
A: log₃(1) = 0 because any number raised to the power of 0 equals 1.

Q3: Can I calculate logarithms with base 3 on a regular calculator?
A: Yes, using the change of base formula: log₃(x) = ln(x)/ln(3) or log(x)/log(3).

Q4: What is the domain of log₃(x)?
A: The function is defined only for x > 0.

Q5: How is log₃(x) different from log₁₀(x)?
A: They measure different exponential relationships. log₃(x) grows faster than log₁₀(x) because 3 < 10.