Find the positive solution of the equation. 8x^((8)/(5))-22=52466 Answer:

Add 22 to isolate variable: Add 22 to both sides of the equation to isolate the term with the variable on one side. \[8x^{\frac{8}{5}} - 22 + 22 = 52466 + 22\] \[8x^{\frac{8}{5}} = 52488\]Divide by 8: Divide both sides of the equation by 8 to solve for $x^{\frac{8}{5}}$. \[\frac{8x^{\frac{8}{5}}}{8} = \frac{52488}{8}\] \[x^{\frac{8}{5}} = 6561\]Recognize power of 3: Recognize that 6561 is a power of 3. Specifically, $6561 = 3^8$. \[x^{\frac{8}{5}} = 3^8\]Take fifth root: Take the fifth root of both sides of the equation to solve for $x^{\frac{8}{5} \cdot \frac{5}{8}}$. \[\left(x^{\frac{8}{5}}\right)^{\frac{5}{8}} = \left(3^8\right)^{\frac{5}{8}}\] \[x = 3^5\]Calculate x value: Calculate $3^5$ to find the value of x. \[3^5 = 3 \times 3 \times 3 \times 3 \times 3\] \[3^5 = 243\]

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Q. Find the positive solution of the equation.

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8 x^{\frac{8}{5}}-22=52466

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Answer:

Add $22$ to isolate variable: Add $22$ to both sides of the equation to isolate the term with the variable on one side. $\newline$ $8x^{\frac{8}{5}} - 22 + 22 = 52466 + 22$ $\newline$ $8x^{\frac{8}{5}} = 52488$
Divide by $8$ : Divide both sides of the equation by $8$ to solve for $x^{\frac{8}{5}}$ . $\newline$ $\frac{8x^{\frac{8}{5}}}{8} = \frac{52488}{8}$ $\newline$ $x^{\frac{8}{5}} = 6561$
Recognize power of $3$ : Recognize that $6561$ is a power of $3$ . Specifically, $6561 = 3^8$ . $\newline$ $x^{\frac{8}{5}} = 3^8$
Take fifth root: Take the fifth root of both sides of the equation to solve for $x^{\frac{8}{5} \cdot \frac{5}{8}}$ . $\newline$ $\left(x^{\frac{8}{5}}\right)^{\frac{5}{8}} = \left(3^8\right)^{\frac{5}{8}}$ $\newline$ $x = 3^5$
Calculate x value: Calculate $3^5$ to find the value of x. $\newline$ $3^5 = 3 \times 3 \times 3 \times 3 \times 3$ $\newline$ $3^5 = 243$