Log Equation Solver Calculator

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

About Log Equation Solver Calculator

To undo a logarithm, exponentiate both sides. From k·log_b(x) = c divide by k and then raise b to that power, giving x = b^(c/k).

Formula

Log equation

k·log_b(x) = c ⇒ x = b^(c/k)

Worked example

With the default values below, Log Equation Solver Calculator returns x of 81.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Base b in log_b(x) = cminimum 0: 3
Right-hand side c: 4
Coefficient k in k·log_b(x) = c: 1

Results

x: 81.00000000
Exponent c/k: 4.00000000
k·log_b(x) at the solution: 4.00000000
Base used: 3.000000

Step by step

1Values used
2Log equation
3x= 81.00000000
4Exponent c/k= 4.00000000
5k·log_b(x) at the solution= 4.00000000
6Base used= 3.000000

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 log₃(x) = 4.

x = 3⁴ = 81.

Do I need to check the solution?

Yes when the original equation has sums of logs, because the algebra can introduce values that make an argument non-positive.