Exponential Equation Solver Calculator

Work out exponential equation solver instantly with clear inputs, formula shown and shareable results.

About Exponential Equation Solver Calculator

Divide by the coefficient to isolate the exponential, then take logarithms of both sides. Since log(bˣ) = x·log b, that gives x = log(c/a) / log b.

Formula

Exponential equation

a·bˣ = c ⇒ x = log(c/a) / log(b)

Worked example

With the default values below, Exponential Equation Solver Calculator returns x of 5.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Coefficient a in a·bˣ = c: 3
Base bminimum 0: 2
Right-hand side c: 96

Results

x: 5.00000000
c ÷ a: 32.00000000
a·bˣ at the solution: 96.000000
Increase in x that doubles the value: 1.00000000

Step by step

1Values used
2Exponential equation
3x= 5.00000000
4c ÷ a= 32.00000000
5a·bˣ at the solution= 96.000000
6Increase in x that doubles the value= 1.00000000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Solve 3 × 2ˣ = 96.

2ˣ = 32, so x = 5.

Why must c/a be positive?

Because bˣ is positive for every real x when b is positive, so a negative or zero ratio has no real solution.