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Math

Exponential Equation Calculator

Solve a positive-base equation b^x = y for its real exponent.

Exact method explained belowEditable inputs
Calculation notebook
Calculation notebook

The formula and worked example below explain the calculation.

See the method

Enter your values

Runs on your device

Your answer

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter base b, target y.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

For positive b ≠ 1 and y > 0, take logarithms of both sides to obtain x = ln(y)/ln(b). Base 1 is handled as an identity or contradiction.

A WORKED EXAMPLE

Using base b = 2, target y = 32, the result is 5. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Not in this real logarithmic model. Negative bases have different real-domain restrictions depending on whether the exponent is integer or rational.

What to keep in mind

Positive real base and target only. Bases extremely close to one amplify numerical error. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.

Common questions

Can the base be negative?

Not in this real logarithmic model. Negative bases have different real-domain restrictions depending on whether the exponent is integer or rational.

How can I check the result?

For positive b ≠ 1 and y > 0, take logarithms of both sides to obtain x = ln(y)/ln(b). Base 1 is handled as an identity or contradiction. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.

Methodology maintained by ClarityKit. How these tools are built and checked.