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

May 21, 2026Mathematics

ScanSolve AI Answer

May 21, 2026

Answer

-\frac{1}{4} $, find the values of$ x$.

Here are the solutions for both parts of the problem.

a) Given the equation $\log_7 (x^2 - 5x + 1)^{\frac{1}{4}} = -\frac{1}{4}$ , find the values of $x$ .

Step 1: Use the logarithm property $\log_b (A^c) = c \log_b A$ to simplify the left side of the equation. $\frac{1}{4} \log_7 (x^2 - 5x + 1) = -\frac{1}{4}$

Step 2: Multiply both sides by $4$ . $\log_7 (x^2 - 5x + 1) = -1$

Step 3: Convert the logarithmic equation

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Quick Answer

Use the logarithm property _b (A^c) = c _b A to simplify the left side of the equation.

Asked on May 21, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 21, 2026

Here are the solutions for both parts of the problem. a) Given the equation _7 (x^2 - 5x + 1)^(1)/(4) = -(1)/(4), find the values of x. Step 1: Use the logarithm property _b (A^c) = c _b A to simplify the left side of the equation. (1)/(4) _7 (x^2 - 5x + 1) = -(1)/(4) Step 2: Multiply both sides by 4. _7 (x^2 - 5x + 1) = -1 Step 3: Convert the logarithmic equation