1. What is Logarithm Base 10?

The logarithm base 10 (log₁₀) of a number is the exponent to which 10 must be raised to produce that number. It's commonly used in scientific calculations, pH measurements, and decibel scales.

2. How Does the Calculator Work?

The calculator uses the logarithmic equation:

Where:

• \( x \) — Input value (must be positive)
• \( y \) — Result (exponent to which 10 must be raised to get x)

Explanation: For example, log₁₀(100) = 2 because 10² = 100.

3. Importance of Logarithms

Details: Logarithms are essential in mathematics and science for handling very large or small numbers, solving exponential equations, and in many real-world applications like measuring earthquake intensity (Richter scale) or sound loudness (decibels).

4. Using the Calculator

Tips: Enter any positive number to calculate its base-10 logarithm. The input must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between log and ln?
A: log typically means log₁₀ (base 10), while ln means log_e (natural logarithm, base e ≈ 2.71828).

Q2: What is log10(1)?
A: log₁₀(1) = 0, because 10⁰ = 1.

Q3: Can I calculate log of 0 or negative numbers?
A: No, log₁₀(0) is undefined, and logarithms of negative numbers are complex numbers.

Q4: What are common applications of log10?
A: pH calculations, decibel scales, Richter scale for earthquakes, and many scientific measurements.

Q5: How is this different from other logarithmic bases?
A: The base determines what number is raised to the power. Base 10 is particularly useful for decimal-based calculations.