Log Calculator

Enter a positive number and logarithm base to calculate log base b of x.

Stable numericsSubstitute / reconstructIndependent checkLocal calculation

Value x

Base

log₁₀(1000) = 3Base logarithm

6.907755Natural log ln(x)

9.965784log₂(x)

Algebra round-trip cluster

Solve once, then verify the same object through another representation

Independent round trips and invariants expose sign, scaling, reconstruction and degeneracy mistakes that a single formatted answer can hide.

Quadratics Matrices Systems

All 28 algebra tools

Matrix InverseA↔A⁻¹ identity round trips MidpointEndpoint reflection round trip Linear EquationScale invariance + degeneracy classes DeterminantTranspose/row-operation invariants Quadratic VertexStandard ↔ vertex coefficient round trip Slope InterceptPoints ↔ line-form equivalence Polynomial DivisionQuotient/remainder reconstruction Standard FormSlope-intercept ↔ standard round trip

Log relation solver: log_b(x) = y

Solve for the argument, logarithm or base from the other two values. Domain checks and the equivalent exponential equation make invalid combinations visible.

Solve forBase bArgument xResult y

—Solved value

—Exponential check

Ready.

Transform, then verify

Equivalent forms should agree. Use discriminants, roots, factoring, vertex form, substitution, matrix checks, or the Remainder Theorem where appropriate to verify the result rather than relying on a single opaque output.

Independent algebra verification

The primary calculation is paired with a substitution, invariant, inverse operation, reconstruction, or equivalent-form check so the displayed answer is easier to audit.

Scope and precision

These are bounded browser calculators, not a universal computer algebra system. WebToolArc keeps exact algebraic identities visible where practical, uses stable floating-point algorithms for numeric work, distinguishes undefined/no-solution/infinite-solution cases, and shows an independent check after the main Calculate action.