Find the positive solution of the equation. 4x^((5)/(6))+6=4102 Answer:

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Find the positive solution of the equation.  4x^((5)/(6))+6=4102 Answer:

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Isolate variable term: Isolate the term with the variable. Subtract 6 from both sides of the equation to isolate the term with the variable x. 4x^(5/6) + 6 - 6 = 4102 - 6 4x^(5/6) = 4096Subtract to isolate x: Divide both sides by 4 to solve for x^(5/6). 4x^(5/6) / 4 = 4096 / 4 x^(5/6) = 1024Divide to solve x^(5/6): Recognize that 1024 is a power of 2. 1024 is 2 raised to the power of 10 because 2^10 = 1024. x^(5/6) = 2^10Recognize power of 2: Write the equation in terms of a common base. Since we have x^(5/6) = 2^10, we can express x as 2 raised to some power. Let's find the power that 2 must be raised to in order to get x by equating the exponents. (5/6) * (the power of 2 that gives x) = 10Write in common base: Solve for the power of 2 that gives x. Multiply both sides of the equation by 6/5 to solve for the power of 2. (6/5) * (5/6) * (the power of 2 that gives x) = (6/5) * 10 (the power of 2 that gives x) = 12Solve for power of 2: Write x as 2 raised to the power of 12. Since the power of 2 that gives x is 12, we can write x as 2^12. x = 2^12Write x as 2^12: Calculate the value of 2^12. 2^12 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 2^12 = 4096

Find the positive solution of the equation. $\newline$ $4 x^{\frac{5}{6}}+6=4102$ $\newline$ Answer:

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Find the positive solution of the equation. $\newline$ $4 x^{\frac{5}{6}}+6=4102$ $\newline$ Answer: