Find the positive solution of the equation. 3x^((9)/(8))+24=5859399 Answer:

Isolate variable term: Isolate the term with the variable. Subtract 24 from both sides of the equation to isolate the term with the variable $x$. $3x^{\frac{9}{8}} + 24 - 24 = 5859399 - 24$ $3x^{\frac{9}{8}} = 5859375$Divide by 3: Divide both sides by 3 to solve for $x^{\frac{9}{8}}$. $\frac{3x^{\frac{9}{8}}}{3} = \frac{5859375}{3}$ $x^{\frac{9}{8}} = 1953125$Recognize power of 5: Recognize that 1953125 is a power of 5. $1953125 = 5^9$Set equal and solve: Set the expression equal to $5^9$ and solve for $x$. Since $x^{\frac{9}{8}} = 5^9$, we can now find $x$ by taking both sides to the power of $\frac{8}{9}$. $(x^{\frac{9}{8}})^{\frac{8}{9}} = (5^9)^{\frac{8}{9}}$ $x = 5^8$Calculate power of 5: Calculate $5^8$. $5^8 = 390625$

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Q. Find the positive solution of the equation.

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3 x^{\frac{9}{8}}+24=5859399

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Answer:

Isolate variable term: Isolate the term with the variable. $\newline$ Subtract $24$ from both sides of the equation to isolate the term with the variable $x$ . $\newline$ $3x^{\frac{9}{8}} + 24 - 24 = 5859399 - 24$ $\newline$ $3x^{\frac{9}{8}} = 5859375$
Divide by $3$ : Divide both sides by $3$ to solve for $x^{\frac{9}{8}}$ . $\newline$ $\frac{3x^{\frac{9}{8}}}{3} = \frac{5859375}{3}$ $\newline$ $x^{\frac{9}{8}} = 1953125$
Recognize power of $5$ : Recognize that $1953125$ is a power of $5$ . $\newline$ $1953125 = 5^9$
Set equal and solve: Set the expression equal to $5^9$ and solve for $x$ . $\newline$ Since $x^{\frac{9}{8}} = 5^9$ , we can now find $x$ by taking both sides to the power of $\frac{8}{9}$ . $\newline$ $(x^{\frac{9}{8}})^{\frac{8}{9}} = (5^9)^{\frac{8}{9}}$ $\newline$ $x = 5^8$
Calculate power of $5$ : Calculate $5^8$ . $\newline$ $5^8 = 390625$