Log Calculator
This free online logarithm calculator solves equations of the form $\log_b(x) = y$ by entering any two of the three values (base, argument, or result). It supports any positive base including $e$, with step-by-step solutions using the change-of-base formula.
How to Use This Calculator
The tool supports three calculation modes determined by which field you leave empty:
1. Find the result (y): Enter the base and argument. The calculator computes $y = \log_b(x)$.
Example: base=10, x=100 → $\log_{10}(100) = 2$
2. Find the argument (x): Enter the base and result. The calculator computes $x = b^y$.
Example: base=2, y=3 → $2^3 = 8$
3. Find the base (b): Enter the argument and result. The calculator computes $b = x^{1/y}$.
Example: x=100, y=2 → $100^{1/2} = 10$
Applications of Logarithms
Logarithms appear throughout science, engineering, and everyday life:
- Science & Engineering: Decibel scale ($\log_{10}$), pH scale ($\log_{10}$), Richter scale ($\log_{10}$)
- Mathematics & Physics: Natural log ($\ln$) in calculus, differential equations, radioactive decay
- Computer Science: Binary log ($\log_2$) in information theory, algorithm analysis, binary search
- Finance: Continuous compounding, logarithmic returns, time value of money
- Data Visualization: Log scales for charts with wide-ranging values
Why Choose This Calculator?
All calculations run entirely in your browser — nothing is sent to any server. Results appear instantly with no page reloads. Step-by-step solutions show the change-of-base formula in action. Supports base $e$, base 10, base 2, or any custom positive base.
Privacy & Performance
100% client-side computation. No data is transmitted, logged, or stored on any server. Free to use with no signup required and no usage limits.
🔒 Client-side only⚡ Web Worker processing🌐 Works offline🛡️ Zero server logs