Logarithmic / Exponential Equation Solver
Solve a·log_base(x) + c = target, a·base^x + c = target, or A·e^(kx) = target — pick the equation form.
Result
Solution (x)
1,000.000000
Verify: substitute back into the original equation.
- Equation forma-log-x-eq-target
- a1
- b (base)10
- c0
- Target3.0000
- Solution (x)1,000.00000000
Step-by-step
- 1·log_10(x) + 0 = 3
- → log_10(x) = (3 − 0) / 1 = 3.000000
- → x = 10^3.0000 = 1,000.000000.
How to use this calculator
- Pick the equation form that matches your problem.
- Enter coefficients. Use a=1 and c=0 for the simplest "log_b(x) = target" or "b^x = target" forms.
- The Steps panel shows the algebra; verify by substituting the solution back.
About this calculator
Closed-form solvers for the most common logarithmic and exponential equation forms. The key identity is that log and exp are mutual inverses: x = b^y ⇔ y = log_b(x). To solve "a·log_b(x) + c = target", isolate the log and exponentiate: x = b^((target−c)/a). To solve "a·b^x + c = target", isolate the exponential and take log: x = log_b((target−c)/a). For the natural-base form A·e^(kx) = target, x = ln(target/A)/k — used in radioactive-decay, compound-interest, and population-growth problems. The "solve for k" variant given a known time t is useful for fitting an exponential model from two data points.
Frequently asked
When the algebraic isolation yields b^x = (non-positive) or e^(kx) = (non-positive) — exponentials are always strictly positive, so the equation is inconsistent.
Related calculators
Logarithm Calculator
log_b(x) for any base b > 0, b ≠ 1, x > 0. Common bases shown side-by-side.
Antilogarithm Calculator
b^x — the inverse of a logarithm. Given the log value and base, recover the original number.
Exponential Growth Calculator
A = A₀ · e^(kt) for continuous growth, or A = A₀ · (1 + r)^t for discrete.
Exponential Decay Calculator
A = A₀ · e^(-kt). Compute remaining quantity, half-life, or decay constant.
Quadratic Equation Solver
ax² + bx + c = 0 → roots via discriminant. Real or complex.
Percentage Math Calculator
Calculate what X% of a value is, find what percentage one number is of another, or compute the percentage change between two numbers.