Find the positive solution of the equation. 6x^((6)/(7))+24=3188670 Answer:

Subtract 24: Subtract 24 from both sides of the equation to isolate the term with the variable x. 6x^(6/7) + 24 - 24 = 3188670 - 24 6x^(6/7) = 3188646Divide by 6: Divide both sides of the equation by 6 to solve for x^(6/7). (6x^(6/7)) / 6 = 3188646 / 6 x^(6/7) = 531441Recognize power of 3: Recognize that 531441 is a power of 3. Specifically, 531441 is 3 raised to the power of 12, since 3^12 = 531441. x^(6/7) = 3^12Raise to reciprocal power: Raise both sides of the equation to the reciprocal of (6/7) to solve for x. (x^(6/7))^(7/6) = (3^12)^(7/6) x = 3^(12 * 7/6) x = 3^(14)Calculate x value: Calculate 3^14 to find the value of x. 3^14 = 4782969 x = 4782969

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Q. Find the positive solution of the equation.

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6 x^{\frac{6}{7}}+24=3188670

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Answer:

Subtract $24$ : Subtract $24$ from both sides of the equation to isolate the term with the variable $x$ . $\newline$ $6x^{(6/7)} + 24 - 24 = 3188670 - 24$ $\newline$ $6x^{(6/7)} = 3188646$
Divide by $6$ : Divide both sides of the equation by $6$ to solve for $x^{\frac{6}{7}}$ . $\frac{6x^{\frac{6}{7}}}{6} = \frac{3188646}{6}$ $x^{\frac{6}{7}} = 531441$
Recognize power of $3$ : Recognize that $531441$ is a power of $3$ . Specifically, $531441$ is $3$ raised to the power of $12$ , since $3^{12} = 531441$ . $\newline$ $x^{\frac{6}{7}} = 3^{12}$
Raise to reciprocal power: Raise both sides of the equation to the reciprocal of $\frac{6}{7}$ to solve for $x$ . $\left(x^{\frac{6}{7}}\right)^{\frac{7}{6}} = \left(3^{12}\right)^{\frac{7}{6}}$ $x = 3^{12 \cdot \frac{7}{6}}$ $x = 3^{14}$
Calculate $x$ value: Calculate $3^{14}$ to find the value of $x$ . $\newline$ $3^{14} = 4782969$ $\newline$ $x = 4782969$