1. What is the Inverse of a Log Function?

The inverse of a logarithmic function \( f(x) = \log_b(x) \) is the exponential function \( f^{-1}(y) = b^y \). This means that if \( y = \log_b(x) \), then \( x = b^y \).

2. How Does the Calculator Work?

The calculator uses the inverse log formula:

Where:

• \( y \) — The result of the original log function (unitless)
• \( b \) — The base of the logarithm (must be positive and ≠ 1)
• \( f^{-1}(y) \) — The inverse function value (unitless)

Explanation: The calculator raises the base (b) to the power of the input value (y) to find the original number that would produce y when the logarithm is taken with base b.

3. Importance of Inverse Log Calculation

Details: Calculating the inverse of log functions is essential in many scientific and engineering applications, including solving exponential equations, signal processing, and data analysis where logarithmic scales are used.

4. Using the Calculator

Tips: Enter the y value (result of the log function) and the base of the logarithm. The base must be a positive number different from 1.

5. Frequently Asked Questions (FAQ)

Q1: What's the inverse of natural log (ln)?
A: The natural log has base e (≈2.71828), so its inverse is \( e^y \).

Q2: What's the inverse of common log (log₁₀)?
A: The common log has base 10, so its inverse is \( 10^y \).

Q3: Why can't the base be 1?
A: The logarithmic function is not defined for base 1 because \( 1^y \) always equals 1 for any y, making the function not invertible.

Q4: What if my y value is negative?
A: Negative y values are perfectly valid. For example, if y = -2 and b = 10, then \( f^{-1}(y) = 10^{-2} = 0.01 \).

Q5: How is this different from antilog?
A: They are the same concept. "Antilog" is just another term for the inverse log function.