Negative Log Calculator
Calculate negative logarithm -log(x) for any base
Must be a positive number
Common bases: 10 (for pH calculations) or e ≈ 2.718 (natural)
How to Use This Calculator
Enter Number
Input the positive number (x) for which you want to find the negative logarithm. The number must be greater than 0.
Specify Base
Enter the base of the logarithm (default is 10 for common logarithm, used in pH calculations). Use e ≈ 2.71828 for natural logarithms.
Calculate
Click "Calculate -log" to compute the negative logarithm. The result shows -logb(x) = logb(1/x).
Formula
-logb(x) = logb(1/x)
Where:
- x = positive number
- b = base (positive number, not equal to 1)
- -logb(x) = negative logarithm
Example 1: pH Calculation -log₁₀(0.001)
If [H⁺] = 0.001 M, then:
pH = -log₁₀(0.001) = -log₁₀(10⁻³) = -(-3) = 3
This is an acidic solution (pH < 7)
Example 2: -log₁₀(100)
-log₁₀(100) = -log₁₀(10²) = -(2) = -2
Negative log can be negative when the number is greater than 1
Example 3: -log₁₀(0.01)
-log₁₀(0.01) = -log₁₀(10⁻²) = -(-2) = 2
Negative log is positive when the number is between 0 and 1
About Negative Log Calculator
The Negative Log Calculator helps you calculate -logb(x), which equals logb(1/x). Negative logarithms are commonly used in chemistry for pH and pOH calculations, where pH = -log[H⁺] and pOH = -log[OH⁻]. They also appear in other scientific contexts where you need the negative of a logarithm.
When to Use This Calculator
- Chemistry: Calculate pH = -log[H⁺] and pOH = -log[OH⁻]
- Acid-Base Chemistry: Determine acidity or basicity of solutions
- Buffer Solutions: Calculate pH of buffer systems
- Scientific Calculations: Work with negative logarithms in various fields
- Mathematical Problems: Solve equations involving negative logarithms
Why Use Our Calculator?
- ✅ Instant Results: Get accurate negative logarithm calculations immediately
- ✅ Chemistry Focus: Perfect for pH and pOH calculations
- ✅ Multiple Bases: Supports any logarithmic base (10, e, or custom)
- ✅ Educational: Learn about negative logarithms and pH calculations
- ✅ 100% Free: No registration or payment required
- ✅ Accurate: High precision calculations
Common Applications
pH Calculation: If hydrogen ion concentration [H⁺] = 0.0001 M, then pH = -log₁₀(0.0001) = -log₁₀(10⁻⁴) = -(-4) = 4. This is an acidic solution.
pOH Calculation: If hydroxide ion concentration [OH⁻] = 0.01 M, then pOH = -log₁₀(0.01) = -log₁₀(10⁻²) = -(-2) = 2. pH = 14 - pOH = 12 (basic solution).
Buffer pH: For a buffer solution, you might need to calculate pH = -log([H⁺]) using the Henderson-Hasselbalch equation.
Tips for Best Results
- The input number must be positive
- For pH calculations, use base 10 (default)
- Negative log is positive when x < 1 (common in pH calculations)
- Negative log is negative when x > 1
- Remember: -log(1/x) = log(x) and -log(x) = log(1/x)
Frequently Asked Questions
What is negative log used for?
Negative logarithms are primarily used in chemistry for pH and pOH calculations. pH = -log[H⁺] measures acidity, where lower pH means more acidic. They also appear in other scientific contexts.
Can negative log be negative?
Yes! If x > 1, then log(x) is positive, so -log(x) is negative. However, in pH calculations, [H⁺] is usually less than 1, making pH positive (since -log(small number) = positive).
How is negative log related to pH?
pH = -log₁₀[H⁺]. This definition makes pH a convenient scale: pH < 7 is acidic, pH = 7 is neutral, pH > 7 is basic. The negative sign makes the scale intuitive - lower [H⁺] means higher pH.
What's the relationship between -log(x) and log(1/x)?
They're equal! -log(x) = log(1/x). This follows from logarithm properties: -log(x) = -log(x) and log(1/x) = log(x⁻¹) = -log(x).
Why is base 10 used for pH?
Base 10 is conventional and convenient. Most [H⁺] values in chemistry are powers of 10, making calculations easier. For example, [H⁺] = 10⁻³ M gives pH = -log(10⁻³) = 3.