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Given 7 (x2 - 5x + 1)^(1)/(4) = -(1)/(4), find the values of x.

Mathematics

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Here are the solutions for both parts of the problem.

a) Given the equation log⁡7(x2−5x+1)14=−14\log_7 (x^2 - 5x + 1)^{\frac{1}{4}} = -\frac{1}{4}, find the values of xx.

  1. Use the logarithm property log⁡b(Ac)=clog⁡bA\log_b (A^c) = c \log_b A to simplify the left side of the equation.

    14log⁡7(x2−5x+1)=−14\frac{1}{4} \log_7 (x^2 - 5x + 1) = -\frac{1}{4}

  2. Multiply both sides by 4.

    log⁡7(x2−5x+1)=−1\log_7 (x^2 - 5x + 1) = -1

  3. Convert the logarithmic equation

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