Find the positive solution of the equation. 4x^((6)/(7))-26=230 Answer:

Add 26 to isolate: Add 26 to both sides of the equation to isolate the term with the variable. 4x^(6/7) - 26 + 26 = 230 + 26 Simplify the equation. 4x^(6/7) = 256Simplify the equation: Divide both sides of the equation by 4 to solve for x^(6/7). (4x^(6/7)) / 4 = 256 / 4 Simplify the equation. x^(6/7) = 64Divide by 4: Raise both sides of the equation to the reciprocal of 6/7 to solve for x. (x^(6/7))^(7/6) = 64^(7/6) Simplify the exponents on the left side. x = 64^(7/6)Raise to reciprocal: Calculate 64^(7/6). Since 64 is 2 raised to the 6th power (2^6), we can rewrite 64^(7/6) as (2^6)^(7/6). (2^6)^(7/6) = 2^(6 * 7/6) Simplify the exponents. 2^(6 * 7/6) = 2^7 Calculate 2^7. 2^7 = 128

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Q. Find the positive solution of the equation.

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4 x^{\frac{6}{7}}-26=230

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Answer:

Add $26$ to isolate: Add $26$ to both sides of the equation to isolate the term with the variable. $\newline$ $4x^{(6/7)} - 26 + 26 = 230 + 26$ $\newline$ Simplify the equation. $\newline$ $4x^{(6/7)} = 256$
Simplify the equation: Divide both sides of the equation by $4$ to solve for $x^{\frac{6}{7}}$ . $\frac{4x^{\frac{6}{7}}}{4} = \frac{256}{4}$ $\text{Simplify the equation.}$ $x^{\frac{6}{7}} = 64$
Divide by $4$ : Raise both sides of the equation to the reciprocal of $\frac{6}{7}$ to solve for $x$ . $\newline$ $(x^{\frac{6}{7}})^{\frac{7}{6}} = 64^{\frac{7}{6}}$ $\newline$ Simplify the exponents on the left side. $\newline$ $x = 64^{\frac{7}{6}}$
Raise to reciprocal: Calculate $64^{\frac{7}{6}}$ . $\newline$ Since $64$ is $2$ raised to the $6$ th power ( $2^6$ ), we can rewrite $64^{\frac{7}{6}}$ as $(2^6)^{\frac{7}{6}}$ . $\newline$ $(2^6)^{\frac{7}{6}} = 2^{6 \cdot \frac{7}{6}}$ $\newline$ Simplify the exponents. $\newline$ $2^{6 \cdot \frac{7}{6}} = 2^7$ $\newline$ Calculate $2^7$ . $\newline$ $64$ $0$