Find the positive solution of the equation. 3x^((6)/(5))+29=12317 Answer:

Isolate variable term: Isolate the term with the variable. Subtract 29 from both sides of the equation to isolate the term with the variable x. 3x^(6/5) + 29 - 29 = 12317 - 29 3x^(6/5) = 12288Subtract 29: Divide both sides by 3 to solve for x^(6/5). 3x^(6/5) / 3 = 12288 / 3 x^(6/5) = 4096Divide by 3: Recognize that 4096 is a power of 2. 4096 is 2 raised to the 12th power, since 2^12 = 4096. x^(6/5) = 2^12Recognize power of 2: Take the 5th root of both sides to solve for x^6. (x^(6/5))^(5/6) = (2^12)^(5/6) x = 2^(12 * 5/6)Take 5th root: Simplify the exponent on the right side. 12 * 5/6 = 10 x = 2^10Simplify exponent: Calculate 2^10. 2^10 = 1024 x = 1024

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Q. Find the positive solution of the equation.

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3 x^{\frac{6}{5}}+29=12317

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Answer:

Isolate variable term: Isolate the term with the variable. $\newline$ Subtract $29$ from both sides of the equation to isolate the term with the variable $x$ . $\newline$ $3x^{(6/5)} + 29 - 29 = 12317 - 29$ $\newline$ $3x^{(6/5)} = 12288$
Subtract $29$ : Divide both sides by $3$ to solve for $x^{\frac{6}{5}}$ . $\newline$ $\frac{3x^{\frac{6}{5}}}{3} = \frac{12288}{3}$ $\newline$ $x^{\frac{6}{5}} = 4096$
Divide by $3$ : Recognize that $4096$ is a power of $2$ . $4096$ is $2$ raised to the $12$ th power, since $2^{12} = 4096$ . $x^{\frac{6}{5}} = 2^{12}$
Recognize power of $2$ : Take the $5^{\text{th}}$ root of both sides to solve for $x^6$ .
$(x^{(6/5)})^{(5/6)} = (2^{12})^{(5/6)}$
$x = 2^{(12 \cdot 5/6)}$
Take $5$ th root: Simplify the exponent on the right side. $\newline$ $12 \times \frac{5}{6} = 10$ $\newline$ $x = 2^{10}$
Simplify exponent: Calculate $2^{10}$ . $\$2^{10} = 1024$ \) $\$x = 1024$ \)