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Exponent & Logarithm Calculator
Calculate powers, logarithms, natural logs, and square roots
Calculate exponential power (a^b)
How Exponential & Logarithmic Calculations Work
Exponential and logarithmic functions are fundamental mathematical operations that are inverses of each other, widely used in science, engineering, and finance.
Select the mathematical operation you want to perform
Enter the required values in the input fields
Click "Calculate" to compute the result
View the precise result with formula display
Copy the result for use in other applications
Power (Exponentiation):
Formula: a^b = a × a × ... (b times)
Example: 2^3 = 2 × 2 × 2 = 8
Used for exponential growth, compound interest, and scientific notation
Logarithm:
Formula: log_b(n) = x means b^x = n
Common Bases: 10 (common log), e (natural log), 2 (binary log)
Example: log_10(100) = 2 because 10^2 = 100
Natural Logarithm:
Formula: ln(n) = log_e(n)
Base e: Approximately 2.718281828459045
Example: ln(7.389) ≈ 2 because e^2 ≈ 7.389
Square Root:
Formula: √n = x means x^2 = n
Example: √16 = 4 because 4^2 = 16
Special case of exponentiation: √n = n^(1/2)
Real-World Applications:
Finance: Compound interest, investment growth
Science: pH scale, radioactive decay, sound intensity
Engineering: Signal processing, control systems
Computer Science: Algorithm complexity, data compression
Mathematical Properties:
Exponents and logarithms are inverse operations
log_b(1) = 0 for any base b
log_b(b) = 1 for any base b
a^0 = 1 for any a ≠ 0