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Exponential and logarithmic equations

Undo an exponential with a logarithm, and a logarithm with an exponential.

When the unknown is in the exponent, take a logarithm of both sides; the exponent comes down as a multiplier. When the unknown is inside a log, rewrite in exponential form. Always check the domain: logarithms need positive arguments.

Worked example: 2^x = 8

Algebra · Exponential-Equations

Solve 2^x = 8

2^{x} = 8

Step by step

  1. 2^{x} = 8

    Start from the equation as given.

  2. 2^{x} - 8 = 0

    Bring everything to one side.

  3. 2^{x} - 8 = 0

    Isolate the exponential, then take a logarithm of both sides.

  4. x = 3

    Solve for the variable.

Reveal the answer
x = 3

Try your own

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