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Tool 472 · logarithm lab

Solve the logarithm, inspect the rule, see the curve.

Evaluate arbitrary-base logarithms, solve any missing value in bʸ=x, recognize exact integer powers, convert bases, compare common logs, verify logarithm laws, and visualize how the base changes the graph.

Any valid baseSolve bʸ = xExact-power detectionInteractive graph

Core logarithm solver

Fill any two of base, exponent and argument; leave one blank to solve it.

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Domain: for real logarithms, x must be positive, b must be positive, and b ≠ 1. Bases between 0 and 1 are valid and produce decreasing logarithmic functions.

Result

Ready to solve.

logarithm
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ln(x)

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log₁₀(x)

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log₂(x)

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Base behavior

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Calculation steps appear here.

Product rule

Quotient rule

Power rule

Core identities:
logb(x)=y ⇔ bʸ=x
logb(MN)=logbM+logbN
logb(M/N)=logbM−logbN
logb(Mᵏ)=k·logbM
logbx = ln(x)/ln(b)
Calculations use IEEE-754 double precision. Exact-power detection is a verification aid for integer exponents; the displayed decimal result remains the numeric authority for non-exact cases.