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Solve the equation 4 x2 - 64 4 − 1 = 0.

Mathematics

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Here are the solutions to the problems:

: Solve the equation log⁡4x2−6log⁡44−1=0\log_4 x^2 - 6\log_4 4 - 1 = 0.

  1. Apply logarithm properties.

    We use the property log⁡bac=clog⁡ba\log_b a^c = c \log_b a and log⁡bb=1\log_b b = 1.

    2log⁡4x−6(1)−1=02\log_4 x - 6(1) - 1 = 0

  2. Simplify the equation.

    2log⁡4x−6−1=02\log_4 x - 6 - 1 = 0 2log⁡4x−7=02\log_4 x - 7 = 0

  3. Isolate the logarithm term

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